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|---|---|---|---|---|
| 枢機卿 | 1000の | |||
| 序数 | 1000番目 （千分の一） | |||
| 因数分解 | 2 3 × 5 3 | |||
| 約数 | 1、2、4、5、8、10、20、25、40、50、100、125、200、250、500、1000 | |||
| ギリシャ数字 | 、Α´ | |||
| ローマ数字 | ま | |||
| ローマ数字 (ユニコード) | ま、ま、ↀ | |||
| Unicodeシンボル | ↀ | |||
| ギリシャ語の 接頭辞 | チリア | |||
| ラテン語の 接頭辞 | ミリ | |||
| バイナリ | 1111101000 2 | |||
| 三元 | 1101001 3 | |||
| セナリー | 4344 6 | |||
| 八進数 | 1750 8 | |||
| 12進数 | 6B4 12 | |||
| 16進数 | 3E8 16 | |||
| タミル語 | ௲ | |||
| 中国語 | 千 | |||
| パンジャブ語 | ੧੦੦੦ | |||
| デーヴァナーガリー文字 | १००० | |||
| アルメニア語 | Ռ | |||
| エジプトの象形文字 | 𓆼 | |||
無料辞書のウィクショナリーで「thousand」 または「1000」を調べてください。
1000または千は、 999 の次で1001の前の自然数です。ほとんどの英語圏の国では、千の位を区切るコンマやピリオドの有無にかかわらず、 1,000のように表記されます。
1000の集合は、古代ギリシャ語ではキリアドと呼ばれることがあります。[1] 1000年の期間はキリアドと呼ばれることもありますが、ラテン語ではミレニアムと呼ばれることが多いです。1000という数字は、中世の文脈では短い千として表現されることもありますが、その場合はゲルマン人の長い千という概念である1200を区別する必要があるからです。
表記
- 1000を1000で表すと
- 1000 —一般的な表記では、1 の後に 3 つのゼロが続きます。
- 1 × 10 3 —工学表記では、この数値は次の式に一致します。
- 科学的に正規化された指数表記では正確に1 × 10 3。
- 1科学的E表記法では正確にはE+3です。
- SI単位系の 1000 単位の接頭辞は「キロ」で、「k」と省略されます。たとえば、キログラムまたは「kg」は 1000グラムです。これは、SI 以外のコンテキストにも拡張されることがあります。たとえば、「ka」(キロ年) は 1000 年の期間の省略形として使用されます。ただし、コンピューター サイエンスでは、「kilo」はより緩く、2 の 10 乗 (1024) を意味します。
- SI 表記法では、改行なしスペースを3000 ごとの区切り文字として、つまり 1000 の累乗ごとに数字の桁を区切るために使用できます。
- 千の倍数は、最後の 3 つのゼロを文字「K」または「k」に置き換えて表されることがあります。たとえば、$30 000 を「$30k」と書いたり、2000 年のY2Kコンピュータ バグを表したりします。
- 通貨単位、特にドルやポンドの 1,000 単位は、口語でグランドと呼ばれます。米国では、これは接尾辞「G」で省略されることがあります。
プロパティ
1000は10番目の二十四角数、または24角数です。[2]また、16番目の一般化された30角数でもあります。[3]
1000はサイクル長20のウィーナー指数であり、 1～20を底とするピラミッド状に配置されたラベル付きボックスの合計でもある。 [4] [5] [6] [a]
1000はnクイーン問題におけるドーナツ盤の多重度要素であり[8]、それぞれの指標は25 [9]、カウントは51である。[10] [11]
1000は、 50の部分集合の和を含まない厳密な分割の数である。[12]
千角形は1000辺の多角形であり、[13] [14]正規形では次数が 2000である。[b]
トーティエント値
1000の縮小トーティエント値は100 [20]、オイラートーティエントは400 [16]である。
11個の整数のトーティエント値は1000（1111、1255、…、3750）である。[16]
1000はオイラーのトーティエント総和関数 の最初の57個の整数の合計にも等しい。[21]
レップディジット
10進数では、1000の倍数は4桁の繰り返し数のトーティエント値である。[16]
合成数のリストでは、7777は8888の合成指数に非常に近い。8886は7779番目の合成数である。[22]また、[16]
1600 = 40 2 は4000のトーティエント値であり、6000も同様で、その合計は10000です。ここで、6000は9999のトーティエントであり、10 4より1小さいです。[16] [c]
23までの最初の9つの素数の合計は100であり、 は23の整数分割数である。[28]
プライム値
10進数表現も使用して、
- 997は168番目で1000未満の最大の素数である[ 25]。
- 97は100未満の25番目で最大の素数であり、
- 9と7はそれぞれ（4番目に）大きい合成数と10未満の素数である。[22] [25]
一方、10000未満の最大の素数は1229番目の素数である9973である。[25] [d]
1000は、 10進数で最小の数であり、減少した数を連結することで3つの素数を最も速く生成できる数である。 [37]
- 1,000,999
- 1,000,999,998,997
- 1,000,999,998,997,996,995,994,993
これらはすべて素数を表す。[38] [39]
素数853とその素数指数147 [25]を加えると1000となる。
散発的なグループ
1000番目の素数は7919である。これは最小の散在群の位数との差が1である。[40] [41]
1001～1999の範囲の数字
1001年から1099年
- 1001 =球状数(7 × 11 × 13)、五角形数、ペンタトープ数、回文数
- 1002 = スフェニック数、メルテンス関数ゼロ、過剰数、 22の分割数
- 1003 = ある素数pとp番目の素数の積、つまりp = 17。
- 1004 =ヘプタナッチ数[42]
- 1005 = メルテンス関数ゼロ、十角錐数[43]
- 1006 =半素数、2つの異なる孤立した素数（2と503）の積。異常な数。平方のない数。22を正方形に分割する（順序付けられた分割）数。2つの異なるペンタトープ数（5と1001）の和。4 ×5の正方形グリッドグラフ内の無向ハミルトン経路の数。[44]双子素数間の記録的なギャップ。[45] 7つの正の5乗の合計である数。[46] 10進数では、等桁数。裏返すと素数のように見える9001。その立方体は他の立方体と連結可能、1_0_1_8_1_0_8_216（「_」は連結を示す、0 = 0 3、1 = 1 3、8 = 2 3、216 = 6 3）[47]
- 1007 = 8つの正の5乗の合計数[48]
- 1008 = それ以下の素数の数で割り切れる
- 1009 =最小の4桁の素数、基数11、15、19、24、28で回文: (838 11、474 15、2F2 19、1I1 24、181 28 )。これはラッキー素数であり、チェン素数でもある。
- 1010 = 10 3 + 10、[49]メルテンス関数ゼロ
- 1011 = 2 nに 101 が含まれ、11011 が含まれない最大のn、5、10、15、20、25、30、35、40、45、50、55、60、65、70、75 の基数（および他の 202 の基数）におけるハーシャッド数、1 を 16 以下の正の整数の逆数に分割する数、エジプト分数[ 50]
- 1012 =三進数、（32 10）四倍三角数（三角数は253）、[51] 1を17以下の正の整数の逆数に分割する数 エジプト分数[50]
- 1013 =ソフィー・ジェルマン素数、[52] 中心平方数、[53]メルテンス関数ゼロ
- 1014 = 2 10 -10、[54]メルテンス関数ゼロ、連続する三角数78と91の間の非三角数の合計[55]
- 1015 =四角錐数[56]
- 1016 =ミアン・チョウラ数列の要素、[57] ステラ・オクタングラ数、辺の長さが14の立方体の表面点の数[58]
- 1017 = 一般化された三角十角数[59]
- 1018 = メルテンス関数のゼロ、1018 16 + 1は素数である[60]
- 1019 =ソフィー・ジャーメイン素数、[52] セーフ素数、[61] チェン素数
- 1020 =割り切れる数
- 1021 = 1019と双子素数。ラッキー素数でもあります。
- 1022 =フリードマン数
- 1023 = 連続する5つの素数の合計（193 + 197 + 199 + 211 + 223） [62] 7つのセルを持つ3次元 ポリキューブの数[63] 9単体の要素数; 2進数を使用して指で数えることができる最大の数; GPS信号で使用される魔法の数字。
- 1024 = 32 2 = 4 5 = 2 10 、1キロバイトのバイト数です（1999年に、 IECは1024を表すためにキビバイトという造語を作りました。キロバイトは1000ですが、この慣例は広く採用されていません）。1024は最小の4桁の平方数であり、フリードマン数でもあります。
- 1025 =プロス数2 10 + 1。モーザー・ド・ブリュイン数列の要素。4 進数表現 (100001 4 ) には 0 と 1 の数字しか含まれず、4 の異なる累乗の合計 (4 5 + 4 0 ) であるため。ヤコブスタール・ルーカス数。原始ピタゴラス三角形の斜辺。
- 1026 = 2の2つの異なる累乗の合計（1024 + 2）
- 1027 = 最初の 8 つの素数の平方の合計。0 から 9 までの数字のみを使用して、2 進数から 18 進数まで表記できます。
- 1028 = 最初の58個の整数のトーティエント関数の合計。0から9の数字のみを使用して2進数から18進数まで表記できる。素数の数は213以下。[64]
- 1029 = 0 から 9 までの数字のみを使用して、2 進数から 18 進数まで記述できます。
- 1030 = 一般化七角数
- 1031 = 5番目の10進数レプユニットの指数と1の数 素数、[65] ソフィー・ジャーマン素数、[52] スーパー素数、チェン素数
- 1032 = 2の2つの異なる累乗の合計（1024 + 8）
- 1033 = emirp、1031との双子素数
- 1034 = 12の正の9乗の合計[66]
- 1035 =三角数、[67] 六角数[68]
- 1036 = 中心多角形数[69]
- 1037 = Eつまようじ配列の番号[70]
- 1038 = 2つの素数の和がn通りである偶数 [71]
- 1039 = 8n+7の形の素数、 [72] 30の1を含まない分割数、[73] 陳素数
- 1040 = 4 5 + 4 2 : 4の異なる累乗の合計。[74] 6×6×6×6のルービックキューブに含まれるピースの数。
- 1041 = 11の正の5乗の合計[75]
- 1042 = 12の正の5乗の合計[76]
- 1043 =偶数桁の合計と奇数桁の合計が偶数となる数[77]
- 1044 = 4の異なる累乗の合計[74]
- 1045 =八角数[78]
- 1046 = f(q)の係数（3次模擬シータ関数）[79]
- 1047 = 18の厳密な合成を同じ合計を持つ連続した部分列に分割する方法の数[80]
- 1048 = 27を正方形でない部分に分割した数[81]
- 1049 =ソフィー・ジャーマン素数、[52] 高次係数数、[82] チェン素数
- 1050 = 1050 8を10進数にするとプロニック数（552 10）となり、 [83] 29を異なる部分に分割したすべての部分の数[84]
- 1051 =中心五角数、[85] 中心十角数
- 1052 = 9つの正の6乗の合計[86]
- 1053 = 三角マッチ棒数[87]
- 1054 =中心三角数[88]
- 1055 = 12の正の6乗の合計[89]
- 1056 =プロニック数[90]
- 1057 = 中心多角形数[91]
- 1058 = 4つの正の5乗の合計、[92]対角線が46の正方形の面積[93]
- 1059 = n 4が4つの正の4乗の和の形で表される数n [94]
- 1060 = 2から97までの最初の25個の素数の合計（ 100未満の素数の数）[95]および23から131までの連続する10個の素数の6番目の合計。[96]
- 1061 = emirp、1063との双子素数、1000から10000までの素数の数（または、10進数表記の4桁の素数の数）[97]
- 1062 = 2つの回文の合計ではない数[98]
- 1063 =スーパー素数、7つの連続する素数の合計（137 + 139 + 149 + 151 + 157 + 163 + 167）; 壁近くの太陽太陽素数[99]
- 1064 = 2つの正の立方数の合計[100]
- 1065 = 一般化された十二角形[101]
- 1066 = 約数の和が平方数になる数[102]
- 1067 = 45の整数 分割のうち、空の部分または他の部分を割り切れない最小の部分を持つ部分の数[103]
- 1068 = 7つの正の5乗の合計数、[46] 15のすべての分割における部分の合計数[104]
- 1069 =エミルプ[105]
- 1070 = 9つの正の5乗の合計数[106]
- 1071 =七角数[107]
- 1072 =中心七角数[108]
- 1073 = 12の正の5乗の合計数[76]
- 1074 = 2つの回文の合計ではない数[98]
- 1075 = 2つの回文の和でない数[98]
- 1076 = 厳密な木の数 重み11 [109]
- 1077 = 7が他のすべての数字より多い数[110]
- 1078 =負の整数のオイラー変換[111]
- 1079 = すべての正の整数は、最大 1079 個の 10 乗の合計です。
- 1080 = 五角数、[112] 主に合成数[113]
- 1081 = 三角数、[67]パドヴァン数列の要素[114]
- 1082 = 中心多角形数[69]
- 1083 = 4分の3平方、[115] 53を素数に分割する数[116]
- 1084 =六角形の螺旋の3番目のスポーク、 [117] 108464 + 1は素数である
- 1085 = nを異なる部分に分割する数> または = 2 [118]
- 1086 =スミス数、[119]最初の59個の整数に対するトーティエント関数の合計
- 1087 = スーパー素数、いとこ素数、ラッキー素数[120]
- 1088 =八角数、（三角数の結果は136）[121] 2の2つの異なる累乗の和、（1024 + 64）[122]重複数を含めてちょうど7つの素数で割り切れる数[123]
- 1089 = 33 2、九角数、中心八角数、9を掛けると十進数表現の数字が反転する最初の自然数。 [124]
- 1090 = 5つの正の5乗の合計[125]
- 1091 = 1093と従兄弟素数および双子素数
- 1092 = それ以下の素数の数で割り切れる
- 1093 = 最小のヴィーフェリッヒ素数（他に知られているヴィーフェリッヒ素数は3511のみ[126]）、 1091と双子素数であり、星の数である[127]
- 1094 = 9つの正の5乗の合計、[106] 109464 + 1は素数である
- 1095 = 10の正の5乗の合計、[128] 2つの回文の合計ではない数
- 1096 = 16角形数、[129] 18の厳密な立体分割数[130]
- 1097 =エミルプ、[105] チェンプライム
- 1098 = 10進数で9の位を含む9の倍数[131]
- 1099 = 9が他のすべての数字より多い数[132]
1100年から1199年
- 1100 = 61を正方形でない部分に分割した数[133]
- 1101 = 風車番号[134]
- 1102 = 最初の60個の整数のトーティエント関数の合計
- 1103 =ソフィー・ジェルマン素数、[52] バランス素数[135]
- 1104 =キース番号[136]
- 1105 = 33 2 + 4 2 = 32 2 + 9 2 = 31 2 + 12 2 = 23 2 + 24 2、カーマイケル数、 [137] n × nの正規魔方陣の魔定数とn = 13のときのnクイーン問題、十角数、 [138]中心平方数、 [53]フェルマー擬素数[139]
- 1106 = 24個の楕円を描くときに平面を分割する領域の数[140]
- 1107 = 重み8の非同型厳密T 0多重集合分割の数[141]
- 1108 = k64 + 1 が素数となる数 k
- 1109 = フリードランダー・イワニエツ素数、[142] チェン素数
- 1110 = kであって、2 k + 3は素数である[143]
- 1111 = 11 × 101、2つの回文素数の積である回文、[144] レプユニット[145]
- 1112 = k であり、9 k - 2 は素数である[146]
- 1113 = 40の厳密な区分数[147]
- 1114 = 22を無秩序な和の無秩序な積として表す方法の数[148]
- 1115 = 27を素数に分割する数[149]
- 1116 = それ以下の素数の数で割り切れる
- 1117 = 16個のセルを持つ対角対称ポリオミノの数、[150] チェン素数
- 1118 = すべての項が{0,1,...,21}に含まれるユニモジュラー2×2行列の数[151]
- 1119 = 9つのノードを持つ二部グラフの数[152]
- 1120 = k64 + 1 が素数となる数 k
- 1121 = 34 2と 34 4の間にある正方形の数。[153]
- 1122 = プロニック数、[90]それ以下の素数の数で割り切れる
- 1123 =バランスのとれた素数[135]
- 1124 =レイランド数[154] = 2 10 + 10 2、スパイ数
- 1125 =アキレス数
- 1126 = {0, 1, 2, 3, 4, 5}の要素を持つ2×2の非特異整数行列の数[155]
- 1127 = 環状体を46回切断して得られる最大ピース数[156]
- 1128 = 47番目の三角数、[67] 24番目の六角数、[68]その下の素数の数（188 × 6）で割り切れる。[157] 1128は中心電荷が24である最大の頂点作用素代数の次元表現であるD 24である。[158]
- 1129 = 半径19の円内の格子点の数[159]
- 1130 = スキポナッチ数[160]
- 1131 =六角形三角形Tの辺の数(26) [161]
- 1132 = 2色の9つのノードを持ち、そのコンポーネントが完全グラフである単純なラベルなしグラフの数[162]
- 1133 = {1、2、3、4、5、6、7、8、9、10、11、12、13、14、15}のプリミティブ部分列の数[163]
- 1134 = その下の素数の数で割り切れる、三角マッチ棒数[87]
- 1135 =中心三角数[164]
- 1136 = 7-サンレットグラフの独立頂点集合と頂点被覆の数[165]
- 1137 = 双曲パスカルピラミッドのレベル5の頂点の値の合計[166]
- 1138 =ジョージ・ルーカスと彼の会社の作品に繰り返し登場する数字。彼の最初の長編映画「 THX 1138」から始まり、特にスター・ウォーズのDVDのイースターエッグの特別なコードです。
- 1139 =風車グラフのウィーナー指数D(3,17) [167]
- 1140 =四面体数[168]
- 1141 = 7-クネーデル数[169]
- 1142 = n 32 + 1 が素数となる n、[170]スパイ数
- 1143 = 2つのコネクタを持つ8つの要素のセット分割の数[171]
- 1144は双子素数の和ではない[172]
- 1145 = 5-クネーデル数[173]
- 1146は双子素数の和ではない[172]
- 1147 = 31 × 37 （連続する2つの素数の積）[174]
- 1148は双子素数の和ではない[172]
- 1149 = 2つの回文素数の積[175]
- 1150 = 左右対称でない11ダイヤモンドの数。[176]
- 1151 = 22の素数間隔に続く最初の素数、[177] 陳素数
- 1152 =高度にトーティエントな数、[178] 3次元滑らかな数 (2 7 ×3 2 )、対角線の長さが48の正方形の面積、[93] アキレス数
- 1153 =スーパープライム、プロスプライム[179]
- 1154 = 2 × 24 2 + 2 = 辺の長さが24の四面体の表面上の点の数[180]
- 1155 = 2つのサイクルグラフの結合における辺の数、両方とも次数33 [181]
- 1156 = 34 2、八面体数、[182]中心五角形数、[85]中心十一角形数。[183]
- 1157 = a^2+1と表せる素因数を持たず、n^2+1と表せる最小の数。[184]
- 1158 = 辺の長さが17の八面体の表面上の点の数[185]
- 1159 = ミアン・チョウラ数列の要素、[57]中心八面体数[186]
- 1160 =八角数[187]
- 1161 = 最初の26個の素数の合計
- 1162 = 五角数、[112]最初の61個の整数のトーティエント関数の合計
- 1163 = 34 2より大きい最小の素数。[188]ルジャンドル予想を参照。陳素数。
- 1164 = 重み8の正規多重集合を分割する多重集合の連鎖の数。ここで、多重集合が正規とは、正の整数の初期区間にまたがる場合である[189]
- 1165 = 5-クネーデル数[173]
- 1166 = 七角錐数[190]
- 1167 = 1から43までの整数の集合から構成できる有理数の数[191]
- 1168 = アンチシグマ(49) [192]
- 1169 = 非常に高いコトティエント数[82]
- 1170 =全国学術クイズ大会(NAQT) の試合で獲得可能な最高得点
- 1171 = スーパープライム
- 1172 = 合計が14で割り切れる最初の14個の整数の部分集合の数[193]
- 1173 = 9つのノードを持つ平面上の単純な三角分割の数[194]
- 1174 = 16の広範囲に渡って完全に強い正規分布を持つ構成の数
- 1175 = 環状体を47回切断して得られる最大ピース数[156]
- 1176 = 三角数[67]
- 1177 = 七角数[107]
- 1178 = 辺の長さが15の立方体の表面点の数[58]
- 1179 = 7*7バイナリ行列の異なるパーマネントの数[195]
- 1180 = 1000を超える非整数乗への非整数分割の最小数。[196]
- 1181 = 8*10^k-49が素数となる1000以上の最小のk。[197]
- 1182 = 2色のビーズ14個で作れるネックレスの数（裏返せないもの）[198]
- 1183 =五角錐数
- 1184 = 1210との友好的な数[199]
- 1185 = 45を互いに素な2つの部分に分割する数[200]
- 1186 = 15個のセルを持つ対角対称ポリオミノの数、[150] 54を素数に分割する数
- 1187 = 安全素数、[61] スターン素数、[201]バランス素数、[135] チェン素数
- 1188 = 18を含む最初の4桁の18の倍数[202]
- 1189 = 35 2から 35 4までの正方形の数。[153]
- 1190 = プロニック数、[90] 28段のトランプハウスを作るのに必要なカードの数[203]
- 1191 = 35 2 - 35 + 1 = H 35（35番目のホグベン数）[204]
- 1192 = 最初の62個の整数のトーティエント関数の合計
- 1193 = 41193 - 31193 が素数となる数、陳素数
- 1194 = 3×3のチェス盤上で2つのビショップと1つのルークを8回動かして到達できる順列の数[205]
- 1195 = a −1 (n) が整数となる最小の4桁の数はa(n) であり、2*a(n-1) - (-1) n [206]
- 1196 = [207]
- 1197 = 風車番号[134]
- 1198 = 中心七角数[108]
- 1199 = 20番目の結合台形の面積[208]
1200年から1299年
- 1200 =千の位、 120の位が10の位、ゲルマン語族の伝統的な大きな数の計算法、ニールセン視聴率サンプルの世帯数、[209] k64 + 1が素数となる数k
- 1201 = 中心平方数、[53] スーパープライム、中心十角数
- 1202 = 平面を25個の楕円で分割した領域の数[140]
- 1203 : 双曲平面の(2,6,∞)タイリングの座標列の最初の4桁の数字[210]
- 1204 : 7×7×7のマジックキューブのマジック定数[211]
- 1205 = 28を奇数部分の数が1となるような分割数[212]
- 1206 = 29角数[213]
- 1207 = 合成ド・ポリニャック数[214]
- 1208 = 超原始数A006939(3)から始まる厳密な因子連鎖の数[215]
- 1209 = {a,b} が a||b の場合、{3,1} のすべての順序付き空でない部分集合の積: 1209=1*3*13*31
- 1210 = 1184との友好的な数[216]
- 1211 = 合成ド・ポリニャック数[214]
- 1212 = 、ここで[217]の分割数である。
- 1213 =エミルプ
- 1214 = 最初の39個の合成数の合計、[218]スパイ数
- 1215 =六角形三角形Tの辺の数(27) [161]
- 1216 = 九角数[219]
- 1217 =スーパー素数、プロス素数[179]
- 1218 = 三角マッチ棒数[87]
- 1219 =メルテンス関数の零点、中心三角数[164]
- 1220 = メルテンス関数ゼロ、シングルトンを含まない長さ16のバイナリベクトルの数[220]
- 1221 = 最初の2桁と3桁の繰り返し桁の積
- 1222 =六角錐の数
- 1223 =ソフィー・ジェルマン素数、[52]バランス素数、200番目の素数[135]
- 1224 = 2つのサイクルグラフの結合における辺の数、両方とも次数34 [181]
- 1225 = 35 2、正方三角数、[221]六角数、[68]中心八角数、[222]二十角数、[223]六十角数[224]および六十四四角数（124角形）。連続する5つの奇数立方数の合計（1³ + 3³ + 5³ + 7³ + 9³）
- 1226 = 15個のノードを持つルート付きアイデンティティツリーの数[225]
- 1227 = 3つの三角数の和として27通り表現できる最小の数[226]
- 1228 = 最初の63個の整数のトーティエント関数の合計
- 1229 =ソフィー・ジェルマン素数、[52] 0から10000までの素数の数、emirp
- 1230 = マホニアン数: T(9, 6) [227]
- 1231 = 最小の山 emirp、121 なので、最小の山の数は 11 × 11 です。
- 1232 = 7集合を奇数部分に分割したラベル付き順序集合の数[228]
- 1233 = 12 2 + 33 2
- 1234 = 30を細かく分けた部分の数、 [84] 1から4までのすべての数字を含む最小の整数
- 1235 = 重複を除いた最初の4つのフィボナッチ数列を含む[229]
- 1236 = 617 + 619: 双子素数の合計[230]
- 1237 = 2p-1 の形の素数
- 1238 = 31のうち1を含まない部分の数[73]
- 1239 = 3Dのつまようじ番号[231]
- 1240 = 四角錐数[56]
- 1241 =中心立方数、[232]スパイ数
- 1242 = 十角数[138]
- 1243 = 合成ド・ポリニャック数[214]
- 1244 = 25の完全なパーティションの数[233]
- 1245 = 5頂点上のラベル付き全域交差集合系の数。[234]
- 1246 = 38のパーティションの数で、どの部分も2回以上出現しない[235]
- 1247 = 五角数[112]
- 1248 = 2の最初の4つの累乗を連結したもの
- 1249 = emirp、三形数[236]
- 1250 = 対角線の長さが50の正方形の面積[93]
- 1251 = 2 × 25 2 + 1 = 0から25までの整数値を持つ2×2行列式の数[237]
- 1252 = 2 × 25 2 + 2 = 辺の長さが25の四面体の表面上の点の数[180]
- 1253 = 少なくとも1つの別個の部分を持つ23の区画の数[238]
- 1254 = 23を互いに素な部分に分割する数[239]
- 1255 = メルテンス関数ゼロ、23を無秩序な和の無秩序な積として表す方法の数、[148] 23の分割数[240]
- 1256 = 1 × 2 × (5 2 ) 2 + 6、[241]メルテンス関数ゼロ
- 1257 = 半径20の円内の格子点の数[159]
- 1258 = 1 × 2 × (5 2 ) 2 + 8、[241]メルテンス関数ゼロ
- 1259 =非常に高いコトティエント数[82]
- 1260 =高度合成数、[242]プロニック数、[90]最小の吸血鬼数、[243]最初の64個の整数のトーティエント関数の合計、厳密な分割数41 [147]ヨハネの黙示録に2回登場
- 1261 = 星の数、[127]メルテンス関数ゼロ
- 1262 = 36個の円を描くことによって平面を分割する領域の最大数[244]
- 1263 = 辺の長さが27の正四面体の丸められた総表面積[245]
- 1264 = 最初の27個の素数の合計
- 1265 = 同じレベルの頂点が同じ次数を持つ43頂点の根付き木の数[246]
- 1266 = 中心五角数、[85]メルテンス関数ゼロ
- 1267 = 7-クネーデル数[169]
- 1268 = 37を素数に分割した数[247]
- 1269 =テオドロスの螺旋を11回転させるために必要な三角形の最小数[248]
- 1270 = 25 + 24×26 + 23×27、[249]メルテンス関数ゼロ
- 1271 = 最初の40個の合成数の合計[218]
- 1272 = 最初の41個の素数でない数の合計[250]
- 1273 = 19 × 67 = 19 × 素数(19) [251]
- 1274 = 連続する三角数の間の非三角数の合計
- 1275 = 三角数、[67]最初の50個の自然数の和
- 1276 = 25カクテルパーティーグラフ内の冗長性のないセットの数[252]
- 1277 = 長さ 9 の素数星座の始まり(「素数非組」)
- 1278 = 20年後のナラヤナの牛と子牛の数[253]
- 1279 = メルテンス関数ゼロ、メルセンヌ素数指数
- 1280 = メルテンス関数ゼロ、全構成部分の数9 [254]
- 1281 =八角数[187]
- 1282 = メルテンス関数ゼロ、46を互いに素な部分に分割する数[200]
- 1283 = 安全な素数[61]
- 1284 = 641 + 643: 双子素数の合計[230]
- 1285 = メルテンス関数ゼロ、自由ノノミノの数、10セルの平行四辺形ポリオミノの数。[255]
- 1286 = 5つの1×2の長方形（またはドミノ）から形成できる、等価でない連結平面図形の数。各接触する長方形のペアは、長さ1の1辺を共有し、長方形の隣接グラフは木になる[256]
- 1287 = [257]
- 1288 = 七角数[107]
- 1289 = ソフィー・ジェルマン素数、 [52]メルテンス関数ゼロ
- 1290 = 、双子素数の平均[258]
- 1291 = 6 4未満の最大の素数、[259]メルテンス関数ゼロ
- 1292 = phi(1292) = phi(sigma(1292))となる数、[260]メルテンス関数ゼロ
- 1293 = [261]
- 1294 = 辺の長さが14の正八面体の丸められた体積[262]
- 1295 = 2つのサイクルグラフの結合における辺の数、両方とも次数35 [181]
- 1296 = 36 2 = 6 4、最初の 8 つの正の整数の立方体の合計、通常の 8 × 8チェス盤上の長方形の数、Adobe InDesign で許可されている最大フォント サイズ、2 文字の組み合わせの数 (00-ZZ)
- 1297 =スーパー素数、メルテンス関数ゼロ、風車数[134]
- 1298 = 55を素数に分割する数
- 1299 = メルテンス関数ゼロ、最小部分が部分の数以上となる52の分割数[263]
1300年から1399年
- 1300 = 最初の 4 つの 5 乗の合計、メルテンス関数のゼロ、NAQTマッチで可能な最大の勝利マージン、最小の偶数奇数超完全数
- 1301 = 中心平方数、[53]ホナカー素数、[264]ラベルのないノードが13個ある木の数[265]
- 1302 = メルテンス関数ゼロ、六角形三角形の辺の数T(28) [161]
- 1303 = 21n+1と31n+1の形式の素数[266] [267]
- 1304 = 1304 6と 1304 9の合計は 328+976
- 1305 = 三角マッチ棒数[87]
- 1306 = メルテンス関数ゼロ。10進数では、1306の各桁を連続する整数で累乗すると、1306 = 1 1 + 3 2 + 0 3 + 6 4となる。135、175、518、598もこの性質を持つ。中心三角数。[164]
- 1307 = 安全な素数[61]
- 1308 = 最初の65個の整数に対するトーティエント関数の合計
- 1309 = 最初のスフェニック数とそれに続く2つの連続したスフェニック数
- 1310 = 3つの球状数列の真ん中にある最小の数字
- 1311 = 32を他のすべてを分割する部分が存在しない整数分割の数[268]
- 1312 = ミアン・チョウラ系列のメンバー[57]
- 1313 = 14のすべての分割の合計[269]
- 1314 = 41の整数分割のうち、異なる部分が連結しているものの数[270]
- 1315 = 10^(2n+1)-7*10^n-1は素数である。[271]
- 1316 = シグマのオイラー変換(11) [272]
- 1317 = 1317 25進数でその数までの全ての数を連結して割り切れる唯一の奇数4桁の数[273]
- 1318 512 + 1は素数である、[274]メルテンス関数は0である
- 1319 = 安全な素数[61]
- 1320 = 659 + 661: 双子素数の合計[230]
- 1321 = フリードレンダー・イワニエツ素数[142]
- 1322 = 21番目の結合台形の面積[208]
- 1323 =アキレス数
- 1324 = D(n)が1, 2を辞書順に並べたn番目の表現である場合。1324はD(D(x))である最初の1以外の数である[275]
- 1325 =マルコフ数、[276]中心四面体数[277]
- 1326 = 三角数、[67]六角数、[68]メルテンス関数ゼロ
- 1327 = 最初の素数とそれに続く33個の連続する合成数
- 1328 = 最初の66個の整数のトーティエント関数の合計
- 1329 = メルテンス関数のゼロ、最初の41個の合成数の和[218]
- 1330 = 四面体数、[154]は2番目の定義の下で1331とルース・アーロン対を形成する
- 1331 = 11 3は中心七角数であり、[108]は2番目の定義の下で1330とルース・アーロン対を形成する。これはx = 36のとき、 x 2 + x − 1の形の唯一の非自明な立方体である。
- 1332 = プロニック数[90]
- 1333 = 37 2 - 37 + 1 = H 37（37番目のホグベン数）[204]
- 1334 = 37個の円を描くことによって平面を分割する領域の最大数[244]
- 1335 = 五角数、[112]メルテンス関数ゼロ
- 1336 = 1 <= x, y <= 24のgcd(x, y)の合計、[278]メルテンス関数ゼロ
- 1337 = leetと呼ばれる新しい綴りで使用されます。ケルビン単位での金のおおよその融点。
- 1338 = 周期18の貴元素の原子番号、[279]メルテンス関数ゼロ
- 1339 = nを割り切る素数の立方数の和の列に2回現れる最初の4桁の数字[280]
- 1340 = k であり、5 × 2 k - 1 は素数である[281]
- 1341 = 1 つ以上のジャンプが 2 回ある最初の山番号。
- 1342 = , [207]メルテンス関数ゼロ
- 1343 = 切り詰められた六角形[282]
- 1344 = 37 2 - 5 2、1344を素数の平方の差として表す唯一の方法[283]
- 1345 = k、k+1、k+2が2つの素数の積となるようなk [284]
- 1346 = 10個のノードを持つ局所的に分離した根付き木の数[285]
- 1347 = 最初の4つのルーカス数 の連結[286]
- 1348 = 22枚のペニーを1枚または2枚ずつ重ねる方法の数[287]
- 1349 = シュテルン・ヤコブスタール数[288]
- 1350 = 九角数[219]
- 1351 = 28を素数に分割する数[149]
- 1352 = 辺の長さが16の立方体の表面点の数、[58] アキレス数
- 1353 = 2 × 26 2 + 1 = 0から26までの整数値を持つ2×2行列式の数[237]
- 1354 = 2 × 26 2 + 2 = 辺の長さが26の四面体の表面上の点の数[180]
- 1355はレカマンの配列でn = 325,374,625,245に初めて現れます。[289]言い換えると、A057167(1355) = 325,374,625,245 [290] [291]
- 1356は双子素数の和ではない[172]
- 1357 = x 2 + y 2 ≤ 41 2の非負解の数[292]
- 1358 = 辺の長さが28の正四面体の丸められた総表面積[245]
- 1359年はフラウィウス・ヨセフスの篩の42番目の年である[293]
- 1360 = 37 2 - 3 2、1360を素数の平方の差として表す唯一の方法[283]
- 1361 = 34の素数差に続く最初の素数、[177] 中心十角数、3番目のミルズ素数、ホナカー素数[264]
- 1362 = 48の非整数分割数[294]
- 1363 = 14個の物体の円形配置を、隣接する1つ以上の物体のペアを入れ替えて変更する方法の数[295]
- 1364 = ルーカス数[296]
- 1365 = ペンタトープ数[297]
- 1366 = 有馬数。1769年に有馬頼之が中国環パズルの最適解における外環の移動回数としてこの数列を構築したことに由来する[298]
- 1367 = 安全素数、[61]バランス素数、3、9、11個の連続する素数の合計（449 + 457 + 461、131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173、101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151）、[135]
- 1368 = 2つのサイクルグラフの結合における辺の数、両方とも36次[181]
- 1369 = 37 2、中心八角数[222]
- 1370 = σ 2 (37): 37の約数の平方和[299]
- 1371 = 最初の28個の素数の合計
- 1372 =アキレス数
- 1373 = 半径21の円内の格子点の数[159]
- 1374 = すべての項が{0,1,...,23}に含まれるユニモジュラー2×2行列の数[151]
- 1375 = 十角錐数[300]
- 1376 = 原始過剰数（すべての真約数が欠損数である過剰数）[301]
- 1377 = 環状体を51回切断して得られる最大ピース数[156]
- 1378 = 三角数[67]
- 1379 = n × nの通常の魔方陣の魔定数と、n = 14の場合のnクイーン問題。
- 1380 = 4入力の8ステップマッピングの数[302]
- 1381 = 中心五角数[85]メルテンス関数ゼロ
- 1382 = 最初の4桁のテトラキ数[303]
- 1383 = 3 × 461. 10 1383 + 7は素数である[304]
- 1384 = [207]
- 1385 = 上下数[305]
- 1386 = 八角錐数[306]
- 1387 = 2を底とする5番目のフェルマー擬素数、[307] 22番目の中心六角数と19番目の十角数、[138] 2番目のスーパープーレ数。[308]
- 1388 = 4 × 19 2 - 3 × 19 + 1 となり、ウラムの螺旋のx軸上にある[309]
- 1389 = 最初の42個の合成数の合計[218]
- 1390 = 最初の43個の素数でない数の合計[250]
- 1391 = 1から47までの整数の集合から構成できる有理数の数[191]
- 1392 =六角形三角形Tの辺の数(29) [161]
- 1393 = 7-クネーデル数[169]
- 1394 = 最初の67個の整数に対するトーティエント関数の合計
- 1395 =吸血鬼数、[243]ミアン・チョウラ数列のメンバー[57]三角マッチ棒数[87]
- 1396 =中心三角数[164]
- 1397 = [310]
- 1398 = 40の整数分割のうち、異なる部分が連結しているものの数[270]
- 1399 = エミルプ[311]
1400年から1499年
- 1400 = {1, ..., 15}の和のない部分集合の数[312]
- 1401 = 風車番号[134]
- 1402 = 増分差が明確に区別される48の整数分割の数、[313] 8ノードを持つ符号付き木の数[314]
- 1403 = M(x) = 11となる最小のx、ここでM()はメルテンス関数[315]
- 1404 = 七角数[107]
- 1405 = 26 2 + 27 2 , 7 2 + 8 2 + ... + 16 2 , 中心平方数[53]
- 1406 = プロニック数、[90] セミメアンドリック数[316]
- 1407 = 38 2 - 38 + 1 = H 38（38番目のホグベン数）[204]
- 1408 = 38個の円を描くことによって平面を分割する領域の最大数[244]
- 1409 =スーパー素数、ソフィー・ジェルマン素数、[52] 8乗が8つの8乗の和となる最小の数、プロス素数[179]
- 1410 = 46番目のベルヌーイ数の分母[317]
- 1411 = LS(41) [318]
- 1412 = LS(42)、[318]スパイ番号
- 1413 = LS(43) [318]
- 1414 = 素因数の合計に加算すると27回の反復後に素数になる最小の合成数[319]
- 1415 = マホニアン数: T(8, 8) [227]
- 1416 = LS(46) [318]
- 1417 = 32を32で割る部分の数[320]
- 1418 = M(x) = 13となる最小のx、ここでM()はメルテンス関数[315]
- 1419 = ツァイゼル数[321]
- 1420 = 56を素数に分割する数
- 1421 = あらゆる滑らかなコンパクトリーマン29次元多様体が部分多様体として実現可能であるのに十分なユークリッド空間の最大次元、[322]スパイ数
- 1422 = 15の区画の数で、2つの部分がマークされている[323]
- 1423 = 200 + 1223で、200番目の素数は1223です。[324]憎しみのシンボルとしても使用される
- 1424 = x 2 + y 2 ≤ 42 2の非負解の数[292]
- 1425 = 5 進数の自己記述数
- 1426 = 最初の68個の整数に対するトーティエント関数の合計、五角数、[112] 42の厳密な分割数[147]
- 1427 = 1429と双子素数[325]
- 1428 = 6つの内部ノード、または18のエッジを持つ完全な三分木の数[326]
- 1429 = 53を分割した数のうち、最小の部分が部分の数以上となるもの[263]
- 1430 =カタロニア語の数字[327]
- 1431 = 三角数、[67]六角数[68]
- 1432 = パドヴァン系列のメンバー[114]
- 1433 =スーパープライム、ホナカープライム、[264] Microsoft SQL Server データベースへのリモート接続に使用される一般的なポート
- 1434 = 辺の長さが23の正四面体の丸められた体積[328]
- 1435 =ヴァンパイアナンバー; [243]ミリメートル単位の標準鉄道軌間、4フィート8インチに相当+1 ⁄ 2 インチ (1.435 m)
- 1436 = 実数3次体の判別式[329]
- 1437 = 複雑さが20の最小の数: +、*、^を使用して構築するのに20個の1を必要とする最小の数[330]
- 1438 = k であり、5 × 2 k - 1 は素数である[281]
- 1439 = ソフィー・ジャーメイン素数、[52]安全素数[61]
- 1440 =高度にトーティエントな数[178] 、大部分が合成数[113]、481角形数。また、1日の分数、標準的なブロックサイズ3+1/2 フロッピーディスク、およびWXGA(II)コンピュータディスプレイの水平解像度
- 1441 = 星番号[127]
- 1442 = 31を個別の部分に分割したすべてのパーティション内の部分の数[84]
- 1443 = 10進数で表した3桁の交換可能な素数の2番目の3つである337、373、733の合計。また、 2つのサイクルグラフの結合における辺の数でもあり、どちらも順序は37である[181 ]
- 1444 = 38 2、ローマ数字の最小のパンデジタル数
- 1445 = [331]
- 1446 = 辺の長さが19の八面体の表面上の点の数[185]
- 1447 =スーパープライム、ハッピーナンバー
- 1448 = phi(prime(k))が平方数となる数k [332]
- 1449 =ステラ・オクタングラ番号
- 1450 = σ 2 (34): 34の約数の平方和[299]
- 1451 = ソフィー・ジェルマン・プライム[52]
- 1452 = 完全グラフK 12の最初のザグレブ指数[333]
- 1453 = 1459のセクシーな素数
- 1454 = 3 × 22 2 + 2 = 辺の長さが22の四角錐の表面上の点の数[334]
- 1455 = kであり、phi(k)とsigma(k)の幾何平均は整数である[335]
- 1456 = 全ての対角線が描かれた正15角形の領域の数[336]
- 1457 = 2 × 27 2 − 1 = 双子の正方形[337]
- 1458 =0と1の11行11列の行列の最大行列式、 3次元平滑数（2×3 6）
- 1459 = 1453 のセクシー素数、9 つの連続する素数の合計 (139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181)、ピアポント素数
- 1460 = 1 年分の閏日を積算するためにユリウス暦で経過しなければならない年数。
- 1461 = 38を素数に分割した数[247]
- 1462 = (35 - 1) × (35 + 8) = 35頂点のホイールグラフの最初のザグレブ指数[338]
- 1463 = 16のすべてのパーティション内の部分の合計数[104]
- 1464 = 辺の長さが13の正二十面体の丸められた総表面積[339]
- 1465 = 5-クネーデル数[173]
- 1466 = 、ここで= [340]の約数の個数
- 1467 = クランクがゼロの39のパーティションの数[341]
- 1468 = 平行移動によって平面を敷き詰める11個のセルを持つポリヘキサゴンの数[342]
- 1469 = 八面体数、[182]高次数[82]
- 1470 =五角錐数、[343]最初の69個の整数に対するトーシェント関数の合計
- 1471 =素数、中心七角数[108]
- 1472 = 15のオーバーパーティション数[344]
- 1473 = 切り詰められた六角形[282]
- 1474 = : 三角数プラス四分の一平方数（すなわち、A000217(44) + A002620(44)）[345]
- 1475 = 33を異なる回数だけ分割した数[346]
- 1476 = 核のある完全数[347]
- 1477 = 7-クネーデル数[169]
- 1478 = 11の全構成における最大部品の総数[348]
- 1479 = 平面分割数12 [349]
- 1480 = 最初の29個の素数の合計
- 1481 = ソフィー・ジェルマン・プライム[52]
- 1482 = プロニック数、[90]最大部分が一度だけ現れる15の単峰性構成の数[350]
- 1483 = 39 2 - 39 + 1 = H 39（39番目のホグベン数）[204]
- 1484 = 39個の円を描くことによって平面を分割する領域の最大数[244]
- 1485 = 三角数
- 1486 = 厳密な立体分割の数19 [130]
- 1487 = 安全な素数[61]
- 1488 = 三角マッチ棒数[87]
- 1489 =中心三角数[164]
- 1490 =テトラナッチ数[351]
- 1491 = 九角数、[219]メルテンス関数ゼロ
- 1492 = 実数3次体の判別式、[329]メルテンス関数ゼロ
- 1493 = スターンプライム[201]
- 1494 = 最初の70個の整数に対するトーティエント関数の合計
- 1495 = 9### [352]
- 1496 = 四角錐数[56]
- 1497 = スキポナッチ数[160]
- 1498 = 平らな区画の数41 [353]
- 1499 = ソフィー・ジェルマン素数、[52] スーパー素数
1500年から1599年
- 1500 = 3つの異なるピタゴラス三角形の斜辺[354]
- 1501 = 中心五角数[85]
- 1502 = 連続する整数x、x+1のペアの数で、xとx+1の両方のすべての素因数が最大で47であるもの[355]
- 1503 =テオドロスの螺旋を12回転させるために必要な三角形の最小数[248]
- 1504 = 原始過剰数（すべての真約数が欠損数である過剰数）[301]
- 1505 = 連続する部分の間に明確な違いがある41の整数分割の数[356]
- 1506 = ゴロム分割数28 [357]
- 1507 = 32のうち1を含まない部分の数[73]
- 1508 = 七角錐数[190]
- 1509 = 風車番号[134]
- 1510 =不足数、嫌悪数
- 1511 = ソフィー・ジェルマン素数、[52]バランス素数[135]
- 1512 = kであり、phi(k)とsigma(k)の幾何平均は整数である[335]
- 1513 = 中心平方数[53]
- 1514 = 最初の44個の合成数の合計[218]
- 1515 = あらゆる滑らかなコンパクトリーマン30次元多様体が部分多様体として実現できるユークリッド空間の最大次元[322]
- 1516 = [358]
- 1517 = 半径22の円内の格子点の数[159]
- 1518 = 最初の32個の半素数の和、[359]メルテンス関数のゼロ
- 1519 = 8つのセルを持つポリヘキサゴスの数、[360]メルテンス関数ゼロ
- 1520 = 五角数、[112]メルテンス関数のゼロは、2番目の定義の下で1521とルース・アーロン対を形成する。
- 1521 = 39 2、メルテンス関数ゼロ、中心八角数、[222]は2番目の定義の下で1520とルース・アーロン対を形成する
- 1522 = k であり、5 × 2 k - 1 は素数である[281]
- 1523 =スーパー素数、メルテンス関数ゼロ、安全素数、[61]ミアン・チョウラ数列のメンバー[57]
- 1524 = メルテンス関数 0、k は phi(k) と sigma(k) の幾何平均が整数となる[335]
- 1525 = 七角数、[107]メルテンス関数ゼロ
- 1526 = 交代群Aの共役類の数27 [361]
- 1527 = 2次元分割数11、[362]メルテンス関数0
- 1528 = メルテンス関数ゼロ、辺の長さが21の正八面体の丸められた全表面積[363]
- 1529 = 合成ド・ポリニャック数[214]
- 1530 =吸血鬼の番号[243]
- 1531 = 素数、中心十角数、メルテンス関数ゼロ
- 1532 = 9つのラベルのないエッジを持つ直並列ネットワークの数、[364]メルテンス関数ゼロ
- 1533 = 21 × 73 = 21 × 21番目の素数[251]
- 1534 = 50の非非整数分割数[294]
- 1535 =タビト番号
- 1536 =マイクロプレートの一般的なサイズ、3次元滑らかな数（2 9 ×3）、ちょうど4つの変数の閾値関数の数[365]
- 1537 = キース数、[136]メルテンス関数ゼロ
- 1538 = 辺の長さが17の立方体の表面点の数[58]
- 1539 = 環状体を54回切断して得られる最大ピース数[156]
- 1540 = 三角数、六角数、[68]十角数、[138]四面体数[154]
- 1541 =八角数[187]
- 1542 = kであり、2^kはkから始まる[366]
- 1543 = すべてのフィボナッチ数列を素数で割る、[367]メルテンス関数ゼロ
- 1544 = メルテンス関数ゼロ、17の整数分割の分割数で、すべての部分の長さが同じである[368]
- 1545 = 9個のビーズを3つの異なる色で組み合わせた可逆的なストリング構造の数[369]
- 1546 = 各行と各列に1が1つ以下である5×5の2進行列の数、[370]メルテンス関数ゼロ
- 1547 =六角錐の数
- 1548 = 核心完全数[347]
- 1549 =ド・ポリニャック素数[371]
- 1550 = 1枚のカード幅の平らな屋根を持つ31段のトランプの家を建てるのに必要なカードの数[372]
- 1551 = 6920 - 5369 = A169952(24) - A169952(23) = A169942(24) = 長さ24のゴロム定規の数[373] [374]
- 1552 = 57を素数に分割する数
- 1553 = 509 + 521 + 523 = 連続する3つの素数の和である素数[375]
- 1554 = 2 × 3 × 7 × 37 = 4つの異なる素数の積[376]
- 1555 2を6で割る1554 [377]
- 1556 = 最初の9つの素数の平方の合計
- 1557 = 8つのノードと13のエッジを持つグラフの数[378]
- 1558 = k 64 + 1 が素数となる数 k
- 1559 = ソフィー・ジェルマン・プライム[52]
- 1560 = プロニック数[90]
- 1561 =中心八面体数、[186] 19個のノードを持つ級数縮小木の数[379]
- 1562 = 40個の円を描くことによって平面を分割する領域の最大数[244]
- 1563 = [380]
- 1564 = 最初の71個の整数に対するトーティエント関数の合計
- 1565 =および[381]
- 1566 = k 64 + 1 が素数となる数 k
- 1567 = 少なくとも1つの別個の部分を持つ24の区画の数[238]
- 1568 =アキレス数[382]
- 1569 = 2 × 28 2 + 1 = 0から28までの整数値を持つ2×2行列式の数[237]
- 1570 = 2 × 28 2 + 2 = 辺の長さが28の四面体の表面上の点の数[180]
- 1571 = ホナカー素数[264]
- 1572 = ミアン・チョウラ系列のメンバー[57]
- 1573 = 実数3次体の判別式[329]
- 1574 256 + 1は素数である[383]
- 1575 = 奇数の過剰数、[384]連続する三角数間の非三角数の合計、24の分割数[240]
- 1576 14 == 1 (15^2を法として) [385]
- 1577 = 83の平方剰余の合計[386]
- 1578 = 最初の45個の合成数の合計[218]
- 1579 = 54を分割した数のうち、最小の部分が部分の数以上となるもの[263]
- 1580 = 51の非整数分割数[294]
- 1581 =六角形三角形T(31)の辺の数[161]
- 1582 = 整数三角形[A070080(1582), A070081(1582), A070082(1582)]の面積が整数となる数[387]
- 1583 = ソフィー・ジェルマン
- 1584 = 三角マッチ棒数[87]
- 1585 = リオルダン数、中心三角数[164]
- 1586 = 23番目の結合台形の面積[208]
- 1587 = 3 × 23 2 = 69次の完全三部グラフの辺の数、K 23,23,23 [388]
- 1588 = 最初の72個の整数に対するトーティエント関数の合計
- 1589 = 合成ド・ポリニャック数[214]
- 1590 = 辺の長さが9の正二十面体の丸められた体積[389]
- 1591 = 辺の長さが15の正八面体の丸められた体積[262]
- 1592 = 最初の36個の奇数の約数の合計[390]
- 1593 = 最初の30個の素数の合計
- 1594 = サイズ17の最大高さのハフマン木の最小コスト[391]
- 1595 = 重みが10の非同型集合系の数
- 1596 = 三角数
- 1597 =フィボナッチ素数、[392] マルコフ素数、[276] スーパー素数、emirp
- 1598 = すべての項が{0,1,...,25}に含まれるユニモジュラー2×2行列の数[151]
- 1599 = 2つのサイクルグラフの結合における辺の数、両方とも次数39 [181]
1600年から1699年
- 1600 = 40 2、構造化された大菱形十二面体数、[393] 7 進数の反復数字 (4444 7 )、ホワイト ハウスのペンシルベニア通りの番地、一般的な高校の陸上競技のメートル単位の長さ、 SATの満点(2005 年から 2015 年を除く)
- 1601 = ソフィー・ジェルマン素数、プロス素数、[179]小説『1601年』（マーク・トウェイン）
- 1602 = 辺の長さが20の八面体の表面上の点の数[185]
- 1603 = 非負ランクの27の分割数[394]
- 1604 = 22を素数に分解した数[395]
- 1605 = 7つの正八角形からなるポリオミノの数[396]
- 1606 = 六角錐数[397]
- 1607 = 1609と1613と共にプライムトリプルを構成する[398]
- 1608 = [207]
- 1609 = 切り詰められた六角数[282]
- 1610 = 厳密な区分数43 [147]
- 1611 = 1から51までの整数の集合から構成できる有理数の数[191]
- 1612 = あらゆる滑らかなコンパクトリーマン31次元多様体が部分多様体として実現可能となるのに十分なユークリッド空間の最大次元[322]
- 1613、1607、1619はすべて素数である[399]
- 1614 = 8^1 の分割を 1^8 に細分化する方法の数[400]
- 1615 = 素因数の二乗平均が非素数となる合成数[401]
- 1616 = = {1,2,...,16}内の単調な三つ組(x,y,z)の数3 [402]
- 1617 = 五角数[112]
- 1618 = 中心七角数[108]
- 1619 =二進法の回文素数、安全な素数[61]
- 1620 = 809 + 811: 双子素数の合計[230]
- 1621 =スーパープライム、風車数[134]
- 1622 = 素数 + 1 の形の半素数[403]
- 1623は2つの三角数と4乗の和ではない[404]
- 1624 =アステカダイヤモンドの28次の正方形の数[405]
- 1625 = 中心平方数[53]
- 1626 = 中心五角数[85]
- 1627 = 素数であり、2 × 1627 - 1 = 3253 も素数である[406]
- 1628 = 中心五角数[85]
- 1629 = 辺の長さが24の正四面体の丸められた体積[328]
- 1630 = k^64 + 1 が素数となる数 k
- 1631 = [407]
- 1632 = 正18角形の頂点から作られる鋭角三角形の数[408]
- 1633 = 星番号[127]
- 1634 = 10進数のナルシシズム数
- 1635 = 56の逆数の和が整数になる分割数[409]
- 1636 = x 2 + y 2 ≤ 45 2の非負解の数[292]
- 1637 = 素数島: 隣接する素数がちょうど30離れている最小の素数[410]
- 1638 =調和約数、[411] 5 × 2 1638 - 1 は素数である[281]
- 1639 = 九角数[219]
- 1640 = プロニック数[90]
- 1641 = 41 2 - 41 + 1 = H 41（41番目のホグベン数）[204]
- 1642 = 41個の円を描くことによって平面を分割する領域の最大数[244]
- 1643 = 最初の46個の合成数の合計[218]
- 1644 = 821 + 823: 双子素数の合計[230]
- 1645 = コンウェイのライフゲームにおける回転と反射までの16セルの疑似静物画の数[412]
- 1646 = 8つのノードと14のエッジを持つグラフの数[378]
- 1647と1648はどちらも立方数で割り切れる[413]
- 1648 = 34 3を異なる立方体に分割する数[414]
- 1649 = 高次コトティエント数、[82]レイランド数[154]
- 1650 = 33段のトランプハウスを作るのに必要なカードの数[203]
- 1651 = 七角数[107]
- 1652 = 29を素数に分割する数[149]
- 1653 = 三角数、六角数、[68]半径23の円内の格子点の数[159]
- 1654 = 42を42の約数に分割する数[415]
- 1655 = 辺の長さが6の正十二面体の丸められた体積[416]
- 1656 = 827 + 829: 双子素数の合計[230]
- 1657 =キューバン素数、[417] 2p-1の形の素数
- 1658 = 素因数の合計に加算すると25回の反復後に素数になる最小の合成数[319]
- 1659 = 1から52までの整数の集合から構成できる有理数の数[191]
- 1660 = 最初の73個の整数に対するトーティエント関数の合計
- 1661 = 11 × 151、2つの回文素数の積である回文[144]
- 1662 = 49を互いに素な部分に分割する数[200]
- 1663 = 素数であり、5 1663 - 4 1663は1163桁の素数である[418]
- 1664 = k、k+1、k+2が2つの平方数の和となるようなk [419]
- 1665 = 中心四面体数[277]
- 1666 =ローマ数字における最大の効率的なパンデジタル数（各記号は正確に 1 回出現します）
- 1667 = 228 + 1439であり、228番目の素数は1439である[324]
- 1668 = 33を33と互いに素な部分に分割する数[420]
- 1669 =スーパー素数、次の素数との差がちょうど24である最小の素数[421]
- 1670 = 少なくとも2つの隣接する部分が等しい12の構成の数[422]
- 1671は最初の1671個の合成数の合計を割ります[423]
- 1672 = 41 2 - 3 2、1672を素数の平方の差として表す唯一の方法[283]
- 1673 = RMS番号[424]
- 1674 = kであり、phi(k)とsigma(k)の幾何平均は整数である[335]
- 1675 = 親族番号[425]
- 1676 = 34を異なる回数だけ分割した数[346]
- 1677 = 41 2 - 2 2、1677を素数の平方の差として表す唯一の方法[283]
- 1678 = n 32 + 1が素数となるn [170]
- 1679 = 非常に高いコトティエント数、[82]半素数（23 × 73、アレシボメッセージも参照）、32を異なる部分に分割したすべての部分の数[84]
- 1680 = 高度に合成された数、[242] 2つのサイクルグラフの結合における辺の数、両方とも40次[181]
- 1681 = 41 2 、 n 2 + n + 41の式で得られる素数でない最小の数、中心八角数[222]
- 1682 = そして1683 はルースとアーロンのペアのメンバーです (最初の定義)
- 1683 = 三角マッチ棒数[87]
- 1684 =中心三角数[164]
- 1685 = 5-クネーデル数[173]
- 1686 = [207]
- 1687 = 7-クネーデル数[169]
- 1688 = 1より大きい正の整数の最小公倍数72の有限連結集合の数[426]
- 1689 = [427]
- 1690 = 14を2の累乗に合成した数[428]
- 1691 = 逆さまにすると同じになり、ストロボグラム数になる[429]
- 1692 = 核のある完全数[347]
- 1693 = 41 2より大きい最小の素数。[188]
- 1694 = すべての項が{0,1,...,26}に含まれるユニモジュラー2×2行列の数[151]
- 1695 = n × nの通常の魔方陣の魔法定数とn = 15のときのnクイーン問題。58 を素数に分割する数
- 1696 = 最初の74個の整数に対するトーティエント関数の合計
- 1697 = フリードレンダー-イワニエツ素数[142]
- 1698 = 同じレベルの頂点が同じ次数を持つ47頂点を持つ根付き木の数[246]
- 1699 = 同じレベルの頂点が同じ次数を持つ48頂点の根付き木の数[246]
1700年から1799年
- 1700 = σ 2 (39): 39の約数の平方和[299]
- 1701 = 、十角数、スタートレックのUSSエンタープライズの船体番号
- 1702 = 3つの連続した塩基の回文: 898 14、 787 15、 6A6 16
- 1703 = 1703131131 / 1000077 であり、1703の約数は1703、131、13、1である[430]
- 1704 = 18を2つの部分に分割したときの各部分の平方の合計[431]
- 1705 =トリボナッチ数[432]
- 1706 = 1 + 4 + 16 + 64 + 256 + 1024 + 256 + 64 + 16 + 4 + 1 4の累乗三角形の5行目の和[433]
- 1707 = 30を30で割る部分の数[320]
- 1708 = 2 2 × 7 × 61 素因数の積1 × 1 × 4 × 18が素因数の和2 + 2 + 7 + 61で割り切れる数[434]
- 1709 =真ん中に57 を加えて形成される 8 つの素数列の最初の数。1709、175709、17575709、1757575709、175757575709、17575757575709、1757575757575709、1757575757575709 はすべて素数ですが、1757575757575757575709 = 232433 × 75616446785773 です。
- 1710 = 環状体を57回切断して得られる最大ピース数[156]
- 1711 = 三角数、中心十角数
- 1712 = 29カクテルパーティーグラフ内の冗長性のないセットの数[252]
- 1713 = 12個のノードを持つ非周期根付き木の数[435]
- 1714 = 3×6の正方形のグリッドの18の周囲の点のうちの2つを結ぶ線分を描くことによって形成される領域の数[436]
- 1715 = kであり、phi(k)とsigma(k)の幾何平均は整数である[335]
- 1716 = 857 + 859: 双子素数の合計[230]
- 1717 = 五角数[112]
- 1718 = [437]
- 1719 = 合成ド・ポリニャック数[214]
- 1720 = 最初の31個の素数の合計
- 1721 = 双子素数; 42 2と 42 4の間にある正方形の数。[153]
- 1722 =ギウガ数、[438]プロニック数[90]
- 1723 =スーパープライム
- 1724 = 42個の円を描くことによって平面を分割する領域の最大数[244]
- 1725 = 47 2 - 22 2 = (素数(15)) 2 - (非素数(15)) 2 [439]
- 1726 = 44を互いに素な部分に分割する数[440]
- 1727 = 24番目の結合台形の面積[208]
- 1728 = 1000 を12 進数で表した量、つまり12の立方数(グレート グロスと呼ばれる) であり、したがって 1 立方フィートに含まれる立方インチの数であり、基数 11 (1331 11 ) および 23 (363 23 )
- 1729 =タクシー数、カーマイケル数、ツァイゼル数、中心立方数、ハーディ・ラマヌジャン数。eの10 進展開では、1729 桁目 (または 1728 桁目) から初めて 10 桁すべてが連続して現れます。1979 年、ロック ミュージカル「ヘアー」はニューヨーク市のブロードウェイで 1729 回の公演を経て閉幕しました。12、32、36 進数では回文です。
- 1730 = 3 × 24 2 + 2 = 辺の長さが24の四角錐の表面上の点の数[334]
- 1731 = kであり、phi(k)とsigma(k)の幾何平均は整数である[335]
- 1732 = [441]
- 1733 =ソフィー・ジェルマン素数、基数 3、18、19 で回文。
- 1734 = 辺の長さが17の立方体の表面積[442]
- 1735 = 55を分割した数のうち、最小の部分が部分の数以上となる数[263]
- 1736 = 最初の75個の整数のトーティエント関数の合計、辺の長さが18の立方体の表面点の数[58]
- 1737 = 風車番号[134]
- 1738 = 52の非整数分割数[294]
- 1739 = 30を奇数部分に分割したすべての部分における1の数[443]
- 1740 =アステカダイヤモンドの29次の正方形の数[405]
- 1741 =素数、中心平方数[53]
- 1742 = 平面を30個の楕円で分割した領域の数[140]
- 1743 =風車グラフのウィーナー指数D(3,21) [167]
- 1744 = k、k+1、k+2が2つの平方数の和となるようなk [419]
- 1745 = 5-クネーデル数[173]
- 1746 = 8ノード上の単位距離グラフの数[444]
- 1747 = バランスのとれた素数[135]
- 1748 = 55を55で割る部分の数[445]
- 1749 = 33を他のすべてを分割する部分が存在しない整数分割の数[268]
- 1750 = 3つの異なるピタゴラス三角形の斜辺[354]
- 1751 = 切り詰められた六角形[282]
- 1752 = 79 2 - 67 2、1752を素数の平方の差として表す唯一の方法[283]
- 1753 =バランスのとれた素数[135]
- 1754 = 5*2 k - 1が素数となるk [281]
- 1755 = 50の整数分割のうち、増分差が明確に区別できるものの数[313]
- 1756 = 中心五角数[85]
- 1757 =テオドロスの螺旋を13回転させるために必要な三角形の最小数[248]
- 1758 = [207]
- 1759 =ド・ポリニャック素数[371]
- 1760 = 1マイルのヤード数
- 1761 = k、k+1、k+2が2つの素数の積となるようなk [284]
- 1762 = 長さ12、カーリング数2の2進数列の数[446]
- 1763 = 2つのサイクルグラフの結合における辺の数、両方とも次数41 [181]
- 1764 = 42 2
- 1765 = スタックの数、または15の平面パーティション[447]
- 1766 = 辺の長さが21の八面体の表面上の点の数[185]
- 1767 = σ(28 2 ) = σ(35 2 ) [448]
- 1768 = 交差しない対角線による12角形を8つの多角形に分割する非等価な分割数（回転まで）[449]
- 1769 = 環状体を58回切断して得られる最大ピース数[156]
- 1770 = 三角数、六角数、[68] セブンティーン・セブンティ、オーストラリアの町
- 1771 = 四面体数[154]
- 1772 = 中心七角数、[108]最初の76個の整数のトーティエント関数の合計
- 1773 = アルファベット{1,2,3,4,5}の長さ5の単語のうち、2つの偶数が連続しない単語の数[450]
- 1774 = 15個のノードと5個の葉を持つ根付き恒等木の数[451]
- 1775 = : 最初の10個の素数の山の合計[452]
- 1776 = 24番目の正方形の星の数。[453] 7×7×7×7のルービックキューブに見えるピースの数。
- 1777 = 42 2より大きい最小の素数。[188]
- 1778 = 6kをkで割ったときの余りが22となるような最小のk >= 1 [454]
- 1779 = 非整数分割数53 [294]
- 1780 = E (1, 0)とN (0, 1)をステップとして、対角線y = xを偶数回水平に横切る(0, 0)から(7, 7)までの格子パスの数[455]
- 1781 = eの最初の1781桁は素数となる[456]
- 1782 = 七角数[107]
- 1783 =ド・ポリニャック素数[371]
- 1784 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}の部分集合の数で、異なる要素のペアごとに商が異なるもの[457]
- 1785 = 四角錐数、[56]三角マッチ棒数[87]
- 1786 =中心三角数[164]
- 1787 =スーパー素数、11 個の連続する素数の合計 (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191)
- 1788 = -1、-2、...、-34のオイラー変換[458]
- 1789 = 17に加算される波状和の数（項が交互に増加したり減少したり、またはその逆）[459]
- 1790 = 50を互いに素な2つの部分に分割する数[200]
- 1791 = 最大 4 つの六角数の和として表すことができない最大の自然数。
- 1792 =グランビル数
- 1793 = 半径24の円内の格子点の数[159]
- 1794 = 九角数、[219] 33のうち1を含まない部分の数[73]
- 1795 = 周囲が38の七角形の数[460]
- 1796 = kであり、phi(k)とsigma(k)の幾何平均は整数である[335]
- 1797 = phi(prime(k))が平方数となる数k [332]
- 1798 = 2 × 29 × 31 = 10 2 × 11101 2 × 11111 2であり、素因数を排他的論理和するとゼロになる[461]
- 1799 = 2 × 30 2 − 1 = 双子の正方形[337]
1800年から1899年
- 1800 = 五角錐の数、[343] アキレス数、また、ダ・ポンテのドン・ジョヴァンニでは、ドンナ・エルヴィラと対峙したドン・ジョヴァンニがこれまでに寝た女性の数（レポレッロの集計による）
- 1801 =キューバ素数、5つと9つの連続する素数の合計（349 + 353 + 359 + 367 + 373と179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227）[417]
- 1802 = 2 × 30 2 + 2 = 辺の長さが30の四面体の表面上の点の数、[180] 30の分割数で奇数の部分が1つの部分となるものの数[212]
- 1803 =平行移動や180度回転ではなく、等面体状に平面を敷き詰める10六角形の数（コンウェイ基準） [462]
- 1804 = k^64 + 1 が素数となる数 k
- 1805 = 43 2から 43 4までの間の正方形の数。[153]
- 1806 = プロニック数、[90]シルベスター数列の最初の4項の積、一次擬完全数、[463] nがn番目のベルヌーイ数の分母に等しい唯一の数、[464] シュレーダー数[465]
- 1807 = シルベスター数列の第5項[466]
- 1808 = 43個の円を描くことによって平面を分割する領域の最大数[244]
- 1809 = 最初の17個のスーパー素数の合計[467]
- 1810 = [468]
- 1811 = ソフィー・ジェルマン全盛期
- 1812 = n 32 + 1が素数となるn [170]
- 1813 = 26個のセルを持ち、2つの直交軸を中心に対称なポリオミノの数[469]
- 1814 = 1 + 6 + 36 + 216 + 1296 + 216 + 36 + 6 + 1 = 6の累乗三角形の4行目の和[470]
- 1815 = 多角形連鎖数[471]
- 1816 = 厳密な区分数44 [147]
- 1817 = 20のすべての分割における素数の合計数[472]
- 1818 = n であり、n 32 + 1 は素数である[170]
- 1819 = 最初の32個の素数の合計から32を引いた値[473]
- 1820 = 五角数、[112]ペンタトープ数、[297]ランレングスが弱増加または弱減少する13の構成の数[474]
- 1821 = ミアン・チョウラ系列のメンバー[57]
- 1822 = 43の異なる部分が連結された整数分割の数[270]
- 1823 =スーパープライム、セーフプライム[61]
- 1824 = 43 2 - 5 2、1824を素数の平方の差として表す唯一の方法[283]
- 1825 =八角数[187]
- 1826 = 十角錐数[300]
- 1827 =吸血鬼番号[243]
- 1828 =メアンドリック数、オープンメアンドリック数、eの最初の10桁の10進数に2回現れる
- 1829 = 複合ド・ポリニャック数[214]
- 1830 = 三角数
- 1831 = 次の素数（1847）との差がちょうど16である最小の素数[475]
- 1832 = 最初の77個の整数に対するトーティエント関数の合計
- 1833 = 13個の殻を持つ十面体に含まれる原子の数[476]
- 1834 = 八面体数、[182]最初の5つの素数の立方数の和
- 1835 = [477]の分子の絶対値
- 1836 =陽子の質量が電子の質量より大きい係数
- 1837 = 星番号[127]
- 1838 = すべての項が{0,1,...,27}に含まれるユニモジュラー2×2行列の数[151]
- 1839 = [478]
- 1840 = 43 2 - 3 2、1840を素数の平方の差として表す唯一の方法[283]
- 1841 = 3種類の額面と29枚の切手を使った切手問題の解決、[479]メルテンス関数ゼロ
- 1842 = 11個のノードを持つラベルなしルート付き木の数[480]
- 1843 = k で、phi(k) は完全な立方体である、[481]メルテンス関数はゼロである
- 1844 = 3 7 - 7 3、[482]メルテンス関数ゼロ
- 1845 = 少なくとも1つの素数を含む25の分割数、[483]メルテンス関数ゼロ
- 1846 = 最初の49個の合成数の合計[218]
- 1847 =スーパープライム
- 1848 = 2つのサイクルグラフの結合における辺の数、両方とも次数42 [181]
- 1849 = 43 2、6進数の回文数（= 12321 6）、中心八角数[222]
- 1850 = 59を素数に分割する数
- 1851 = 最初の32個の素数の合計
- 1852 = 5元上の量子数（同型まで）[484]
- 1853 = 27次の素数の原始根の和、[485]メルテンス関数のゼロ
- 1854 = 固定点を持たない7つの要素の順列の数、[486]メルテンス関数ゼロ
- 1855 = ランコントル数: [7] の順列の数で、正確に 1 つの固定点[487]を持つもの
- 1856 = 最初の78個の整数に対するトーティエント関数の合計
- 1857 = メルテンス関数ゼロ、風車数[134]
- 1858 =立体異性体を無視した14炭素アルカンの数 C 14 H 30 [488]
- 1859 = 複合ド・ポリニャック数[214]
- 1860 =アステカダイヤモンドの正方形の数30 [489]
- 1861 = 中心平方数、[53]メルテンス関数ゼロ
- 1862 = メルテンス関数ゼロ、2番目の定義では1863とルース・アーロン対を形成する
- 1863 = メルテンス関数ゼロ、2番目の定義では1862とルース・アーロン対を形成する
- 1864 = メルテンス関数のゼロは素数である[490]
- 1865 = 12345 6 : 最大の6進法メタドローム（6進法で厳密に昇順の数字を持つ数）[491]
- 1866 = メルテンス関数は0、平面分割数は16、行数は最大2 [492]
- 1867 =ポリニャック素数[371]
- 1868 = 複雑さが21の最小の数: +、*、^を使用して構築するのに21個の1を必要とする最小の数[330]
- 1869 = ハルトマン数: S H (7, 4) [493]
- 1870 = 十角数[138]
- 1871 = 2つの連続する双子素数ペアの最初の素数: (1871, 1873) と (1877, 1879) [494]
- 1872 = 完全グラフK 13の最初のザグレブ指数[333]
- 1873年= 21年後のナラヤナの牛と子牛の数[253]
- 1874 = 25番目の結合台形の面積[208]
- 1875 = 50 2 - 25 2
- 1876 = k^64 + 1 が素数となる数 k
- 1877 = 39の分割数（39は部分の積を分割する）[495]
- 1878 = n 32 + 1が素数となるn [170]
- 1879 = 平方指数を持つ素数[496]
- 1880 = ルーカス数の自己畳み込みの10番目の要素[497]
- 1881 =三角錐角柱番号[498]
- 1882 = 4変数の線形分離可能な ブール関数の数[499]
- 1883 = 交代群Aの共役類の数28 [361]
- 1884 = 5*2 k - 1が素数となるk [281]
- 1885 = ツァイゼル数[321]
- 1886 = 6 4を4乗に分割した数[500]
- 1887 =六角形三角形の辺の数T(34) [161]
- 1888 = 原始過剰数（すべての真約数が欠損数である過剰数）[301]
- 1889 = ソフィー・ジェルマン素数、高次コトティエント数[82]
- 1890 = 三角マッチ棒数字[87]
- 1891 = 三角数、連続する 5 つの素数の和 ( 367 + 373 + 379 + 383 + 389 ) 六角数、[68]中心五角数、[85] 中心三角数[164]
- 1892 = プロニック数[90]
- 1893 = 44 2 - 44 + 1 = H 44（44番目のホグベン数）[204]
- 1894 = 44個の円を描くことによって平面を分割する領域の最大数[244]
- 1895 = シュテルン・ヤコブスタール数[288]
- 1896 = ミアン・チョウラ系列のメンバー[57]
- 1897 = パドヴァン数列の要素、[114] 9頂点の三角形のないグラフの数[501]
- 1898 = 数字の合計が26になるnの最小の倍数[502]
- 1899 = 切り詰められた六角形[282]
![{\displaystyle \lfloor {\sqrt[{3}]{13!}}\rfloor }](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f0943f39851d7f678812a33ee092226567c63e4)
1900年から1999年
- 1900 = 素数の個数 <= 2 14。[64] 1900年(映画)または1976年の映画『ノヴェチェント』とも呼ばれる。 1900年は、ソロルド・ゴセットが半正多面体の一覧を発表した年である。また、マックス・ブルックナーが、二十面体の星型配置、例えば斬新な二十面体の最終星型配置などの多面体モデルの研究を発表した年でもある。
- 1901 = ソフィー・ジェルマン素数、中心十角数
- 1902 = 対称平面分割数27 [503]
- 1903 = 一般化されたカタロニア数[504]
- 1904年= 平らな区画の数43 [353]
- 1905 =フェルマー擬素数[139]
- 1906 = 3n -8が素数となる数n [505]
- 1907 = 安全プライム、[61]バランスプライム[135]
- 1908 = 核のある完全数[347]
- 1909 =超完全数[506]
- 1910 = 正確に1つの固定点を持つ13の合成の数[507]
- 1911 = 七角錐数[190]
- 1912 = ポットリミットポーカーでブラインド1枚後の6回目の最大レイズ額[508]
- 1913 =スーパー素数、ホナカー素数[264]
- 1914 = 12個の白い物体と3個の黒い物体の二分分割の数[509]
- 1915 = 位数5の非同型半群の数[510]
- 1916 = 最初の50個の合成数の合計[218]
- 1917 = 51を互いに素な部分に分割する数[200]
- 1918 = 七角数[107]
- 1919 = 10進数で周期の長さ36の逆数となる最小の数[511]
- 1920 = 連続する三角数間の非三角数の合計
- 1921 = 4次元中心立方数[512]
- 1922 = 対角線の長さが62の正方形の面積[93]
- 1923 = 2 × 31 2 + 1 = 0から31までの整数値を持つ2×2行列式の数[237]
- 1924 = 2 × 31 2 + 2 = 辺の長さが31の四面体の表面上の点の数[180]
- 1925 = 24を無秩序な和の無秩序な積として表す方法の数[148]
- 1926 = 五角数[112]
- 1927 = 2 11 - 11 2 [513]
- 1928 = 2^2^...^2 が取る異なる値の数（13 個の 2 と括弧をあらゆる方法で挿入した場合）[514]
- 1929 = メルテンス関数ゼロ、異なる部分が連結された42の整数分割の数[270]
- 1930 = 連続する整数x、x+1のペアの数で、xとx+1の両方のすべての素因数が最大53であるもの[355]
- 1931年= ソフィー・ジェルマン全盛期
- 1932 = 40を素数部に分割した数[247]
- 1933 = 中心七角数、[108]ホナカー素数[264]
- 1934 = 最初の 79 個の整数に対するトーティエント関数の合計
- 1935 = 2つのサイクルグラフの結合における辺の数、両方とも次数43 [181]
- 1936 = 44 2、18角数、[515] 324角数。
- 1937 = 12次元空間のキラルnオミノの数、1つのセルにラベル[516]
- 1938 = メルテンス関数ゼロ、辺の長さが22の八面体の表面上の点の数[185]
- 1939 = 7-クネーデル数[169]
- 1940 = マホーニアン数: T(8, 9) [227]
- 1941 = 円の周りの16点を直線で結んで得られる領域の最大数[517]
- 1942 = 10k + 1、10k + 3、10k + 7、10k + 9、10k + 13が素数となる数k [518]
- 1943 = 異なる14角数の合計ではない最大の数[519]
- 1944 = 3-smooth number (23×35), Achilles number[382]
- 1945 = number of partitions of 25 into relatively prime parts such that multiplicities of parts are also relatively prime[520]
- 1946 = number of surface points on a cube with edge-length 19[58]
- 1947 = k such that 5·2k + 1 is a prime factor of a Fermat number 22m + 1 for some m[521]
- 1948 = number of strict solid partitions of 20[130]
- 1949 = smallest prime > 442.[188]
- 1950 = ,[522] largest number not the sum of distinct pentadecagonal numbers[519]
- 1951 = cuban prime[417]
- 1952 = number of covers of {1, 2, 3, 4}[523]
- 1953 = triangular number
- 1954 = number of sum-free subsets of {1, ..., 16}[312]
- 1955 = number of partitions of 25 with at least one distinct part[238]
- 1956 = nonagonal number[219]
- 1957 = = total number of ordered k-tuples (k=0,1,2,3,4,5,6) of distinct elements from an 6-element set[524]
- 1958 = number of partitions of 25[240]
- 1959 = Heptanacci-Lucas number[525]
- 1960 = number of parts in all partitions of 33 into distinct parts[84]
- 1961 = number of lattice points inside a circle of radius 25[159]
- 1962 = number of edges in the join of the complete graph K36 and the cycle graph C36[526]
- 1963! - 1 is prime[527]
- 1964 = number of linear forests of planted planar trees with 8 nodes[528]
- 1965 = total number of parts in all partitions of 17[104]
- 1966 = sum of totient function for first 80 integers
- 1967 = least edge-length of a square dissectable into at least 30 squares in the Mrs. Perkins's quilt problem[529]
- σ(1968) = σ(1967) + σ(1966)[530]
- 1969 = Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize[531]
- 1970 = number of compositions of two types of 9 having no even parts[532]
- 1971 = [533]
- 1972 = n such that is prime[534]
- 1973 = Sophie Germain prime, Leonardo prime
- 1974 = number of binary vectors of length 17 containing no singletons[220]
- 1975 = number of partitions of 28 with nonnegative rank[394]
- 1976 = octagonal number[187]
- 1977 = number of non-isomorphic multiset partitions of weight 9 with no singletons[535]
- 1978 = n such that n | (3n + 5)[536]
- 1979 = number of squares between 452 and 454.[153]
- 1980 = pronic number[90]
- 1981 = pinwheel number[134]
- 1982 = maximal number of regions the plane is divided into by drawing 45 circles[244]
- 1983 = skiponacci number[160]
- 1984 = 11111000000 in binary, see also: 1984 (disambiguation)
- 1985 = centered square number[53]
- 1986 = number of ways to write 25 as an orderless product of orderless sums[148]
- 1987 = 300th prime number
- 1988 = sum of the first 33 primes
- 1989 = number of 9-step mappings with 4 inputs[302]
- 1990 = Stella octangula number
- 1991 = 11 × 181, the 46th Gullwing number,[537] palindromic composite number with only palindromic prime factors[538]
- 1992 = number of nonisomorphic sets of nonempty subsets of a 4-set[539]
- 1993 = a number with the property that 41993 - 31993 is prime,[540] number of partitions of 30 into a prime number of parts[149]
- 1994 = Glaisher's function W(37)[541]
- 1995 = number of unlabeled graphs on 9 vertices with independence number 6[542]
- 1996 = a number with the property that (1996! + 3)/3 is prime[543]
- 1997 = [544]
- 1998 = triangular matchstick number[87]
- 1999 = centered triangular number[545] number of regular forms in a myriagram.
Prime numbers
There are 135 prime numbers between 1000 and 2000:[546][547]
- 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999
Notes
- ^ 1000 is the fourth Wiener index of the grid where is the path graph on four vertices.[7] A connected graph with a given Wiener index represents the sum of the distances between all unordered pairs of vertices in said graph.
- ^ In the sequence of regular 1000-gonal numbers of the form , the first non-trivial solution is 2997.[13] In Chowla's function, that counts the sum of divisors except for and , 2997 is the first number to have a value of 1600,[15] which is the Euler totient of 4000 and 6000,[16] while the fifth member in the sequence 9985 (that follows 0, 1, 1000, 2997 and 5992)[13] has an average of divisors that is 2997;[17][18] with 5992 ÷ 2 = 2996, and 1000 + 2997 + 5992 = 9989 (a difference of 4 from the fourth member, after 1).
There are 499 regular star polygrams to the regular chiliagon: 300 are regular compound star forms — a count that represents the twenty-fourth triangular number[19] — with the remaining 199 forms represented by simple regular star polygons. - ^ 1600, a repdigit in septenary (44447),[23] is the composite index of 1891, in turn the like-index of 2223.[22]
2222 and 8888 are both numbers n such that n − 1 is prime (as with 4, 44, 444, and 888),[24] yielding respectively the 331st and 1107th prime numbers,[25] where the former (2221) is also the 64th super-prime.[26] These two prime indexes collectively have a range of 777 integers (1107 : 331), which as a number is also a repdigit in senary.[27] - ^ The sum (2 + 3 + 5 + ... + 29) of the first 10 prime numbers is 129, which is the 97th indexed composite number.[29][22] 9973 is also the 201st super-prime,[26] where 1000 − 201 = 799, which is the smallest number in decimal to have a digit sum of 25,[30] and the mirror permutation of digits of 997.
When splitting four-digit 9973 into two two-digit numbers, 99 and 73, the latter is the composite index of 99, that, when added together is 172, the one hundred and thirty-second composite, with 132 itself the 99th composite;[22] 73 is the twenty-first prime number.[25]
1601 is the 252nd prime,[25] itself a value with a composite index of 197,[22] where 1601 is the 40th and largest consecutive prime lucky number of Euler of the form n2 + n + 41.[31][32] The number of 4-digit prime numbers, in decimal, is its mirror permutation of digits 1061, the 172nd prime.[33]
Also, 7, 97 and 997 are all three respectively at a difference of 3 from 10, 100 and 1000, where, on the other hand, 9973 is 27 = 33 away from 10000.
8 as a binary number is "1000",[34] and this representation, when written in factorial base, is equivalent to 2410.[35] In primorial base, it is equal to 3010.[36]
References
Wikimedia Commons has media related to 1000 (number).
- ^ "chiliad". Merriam-Webster. Archived from the original on 25 March 2022.
- ^ Sloane, N. J. A. (ed.). "Sequence A051876 (24-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A316729 (Generalized 30-gonal (or triacontagonal) numbers: m*(14*m - 13) with m equal to 0, +1, -1, +2, -2, +3, -3, ...)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A034828 (a(n) equal to floor(n^2/4)*(n/2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Ngaokrajang, Kival. Sloane, N. J. A. (ed.). "Illustration for n equal to 1..10 [A034828]". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Janjic, M.; Petkovic, B. (2013). "A Counting Function". pp. 14, 15. arXiv:1301.4550 [math.CO]. Bibcode:2013arXiv1301.4550J
- ^ Sloane, N. J. A. (ed.). "Sequence A143945 (Wiener index of the grid P_n x P_n, where P_n is the path graph on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A054501 (Multiplicity sequence for classification of nonattacking queens on n X n toroidal board)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A054500 (Indicator sequence for classification of nonattacking queens on n X n toroidal board)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A054502 (Counting sequence for classification of nonattacking queens on n X n toroidal board)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ I. Rivin, I. Vardi and P. Zimmermann (1994). The n-queens problem. American Mathematical Monthly. Washington, D.C.: Mathematical Association of America. 101 (7): 629–639. doi:10.1080/00029890.1994.11997004 JSTOR 2974691
- ^ Sloane, N. J. A. (ed.). "Sequence A364349 (Number of strict integer partitions of n containing the sum of no subset of the parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A195163 (1000-gonal numbers: a(n) equal to n*(499*n - 498))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Aṣiru, Muniru A. (2016). "All square chiliagonal numbers". International Journal of Mathematical Education in Science and Technology. 47 (7). Oxfordshire: Taylor & Francis: 1123–1134. Bibcode:2016IJMES..47.1123A. doi:10.1080/0020739X.2016.1164346. MR 3528540. S2CID 123953958. Zbl 1396.97005.
- ^ Sloane, N. J. A. (ed.). "Sequence A048050 (Chowla's function: sum of divisors of n except for 1 and n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A000010 (Euler totient function phi(n): count numbers <= n and prime to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003601 (Numbers n such that the average of the divisors of n is an integer: sigma_0(n) divides sigma_1(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A102187 (Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers: a(n) is the binomial(n+1,2): n*(n+1)/2 equal to 0 + 1 + 2 + ... + n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002322 (Reduced totient function psi(n): least k such that x^k is congruent 1 (mod n) for all x prime to n; also known as the Carmichael lambda function (exponent of unit group mod n); also called the universal exponent of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002088 (Sum of totient function: a(n) is Sum_{k equal to1..n} phi(k), cf. A000010)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
- ^ Sloane, N. J. A. (ed.). "Sequence A048332 (Numbers that are repdigits in base 7)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A028987 (Repdigit - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A006450 (Prime-indexed primes: primes with prime subscripts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A048331 (Numbers that are repdigits in base 6)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A366581 (a(n) = phi(p(n)), where phi is Euler's totient function (A000010) and p(n) is the number of partitions of n (A000041))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A127337 (Numbers that are the sum of 10 consecutive primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A051885 (Smallest number whose sum of digits is n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A202018 (a(n) equal to n^2 + n + 41)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005846 (Primes of the form n^2 + n + 41)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007088 (The binary numbers (or binary words, or binary vectors, or binary expansion of n): numbers written in base 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007623 (Integers written in factorial base)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A049345 (n written in primorial base)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "1000". Prime Curious!. Archived from the original on 25 March 2022.
- ^ Sloane, N. J. A. (ed.). "Sequence A152396 (Let f(M,k) denote the decimal concatenation of k numbers starting with M: M | M-1 | M-2 | ... | M-k+1, k greater than 1. Then a(n) is the smallest M such that for all m in {1,..,n} an m-th prime occurs as f(M,k) for the smallest possible k, order prioritized m equal to 1 through n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A227949 (Primes obtained by concatenating decremented numbers starting at a power of 10)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Ronan, Mark (2006). Symmetry and the Monster: One of the Greatest Quests of Mathematics. New York: Oxford University Press. pp. vii, 1–255. doi:10.1007/s00283-008-9007-9. ISBN 978-0-19-280722-9. MR 2215662. OCLC 180766312. Zbl 1113.00002.
- ^ Sloane, N. J. A. (ed.). "Sequence A001228 (Orders of sporadic simple groups)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A122189 (Heptanacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A332307 (Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n grid graph)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 8 January 2023.
- ^ Sloane, N. J. A. (ed.). "Sequence A036063 (Increasing gaps among twin primes: size)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A003352 (Numbers that are the sum of 7 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A061341 (A061341 Numbers not ending in 0 whose cubes are concatenations of other cubes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003353 (Numbers that are the sum of 8 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A034262 (a(n) = n^3 + n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A020473 (Egyptian fractions: number of partitions of 1 into reciprocals of positive integers <= n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A046092 (4 times triangular numbers: a(n) = 2*n*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
- ^ a b c d e f g h i j k l m n o Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes p: 2p+1 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000325 (a(n) = 2^n - n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006002 (a(n) = n*(n+1)^2/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A005897 (6*n^2 + 2 for n > 0)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A316729 (Generalized 30-gonal (or triacontagonal) numbers: m*(14*m - 13) with m = 0, +1, -1, +2, -2, +3, -3)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006313 (Numbers n such that n^16 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i j k l Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes p: (p-1)/2 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A034964 (Sums of five consecutive primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000162 (Number of 3-dimensional polyominoes (or polycubes) with n cells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A007053 (Number of primes <= 2^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A004023 (Indices of prime repunits: numbers n such that 11...111 (with n 1's)... is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A004801 (Sum of 12 positive 9th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A161328 (E-toothpick sequence (see Comments lines for definition))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A023036 (Smallest positive even integer that is an unordered sum of two primes in exactly n ways)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007522 (Primes of the form 8n+7, that is, primes congruent to -1 mod 8)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000695 (Moser-de Bruijn sequence: sums of distinct powers of 4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003356 (Numbers that are the sum of 11 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A003357 (Numbers that are the sum of 12 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A036301 (Numbers whose sum of even digits and sum of odd digits are equal)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000025 (Coefficients of the 3rd-order mock theta function f(q))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A336130 (Number of ways to split a strict composition of n into contiguous subsequences all having the same sum)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A073576 (Number of partitions of n into squarefree parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers: records for a(n) in A063741)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Base converter | number conversion".
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A015723 (Number of parts in all partitions of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003365 (Numbers that are the sum of 9 positive 6th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i j k Sloane, N. J. A. (ed.). "Sequence A045943 (Triangular matchstick numbers: 3*n*(n+1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: a(n) = 3*n*(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003368 (Numbers that are the sum of 12 positive 6th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i j k l m Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: a(n) = n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003349 (Numbers that are the sum of 4 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A001105 (a(n) = 2*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003294 (Numbers k such that k^4 can be written as a sum of four positive 4th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007504 (Sum of the first n primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A127337 (Numbers that are the sum of 10 consecutive primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A035137 (Numbers that are not the sum of 2 palindromes (where 0 is considered a palindrome))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A347565 (Primes p such that A241014(A000720(p)) is +1 or -1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003325 (Numbers that are the sum of 2 positive cubes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A195162 (Generalized 12-gonal numbers: k*(5*k-4) for k = 0, +-1, +-2, ...)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006532 (Numbers whose sum of divisors is a square)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A341450 (Number of strict integer partitions of n that are empty or have smallest part not dividing all the others)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A006128 (Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A006567 (Emirps (primes whose reversal is a different prime))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A003354 (Numbers that are the sum of 9 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A000566 (Heptagonal numbers (or 7-gonal numbers): n*(5*n-3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A273873 (Number of strict trees of weight n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A292457 (Numbers where 7 outnumbers any other digit)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A073592 (Euler transform of negative integers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A077043 ("Three-quarter squares": a(n) = n^2 - A002620(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000607 (Number of partitions of n into prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A056107 (Third spoke of a hexagonal spiral)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A025147 (Number of partitions of n into distinct parts >= 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A033996 (8 times triangular numbers: a(n) = 4*n*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A018900 (Sums of two distinct powers of 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A046308 (Numbers that are divisible by exactly 7 primes counting multiplicity)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001232 (Numbers n such that 9*n = (n written backwards))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003350 (Numbers that are the sum of 5 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 163
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A003154 (Centered 12-gonal numbers. Also star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003355 (Numbers that are the sum of 10 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A051682 (11-gonal (or hendecagonal) numbers: a(n) = n*(9*n-7)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A323657 (Number of strict solid partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A121029 (Multiples of 9 containing a 9 in their decimal representation)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A292449 (Numbers where 9 outnumbers any other digit)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A087188 (number of partitions of n into distinct squarefree parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers: 2*n^2 + 6*n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A002997 : Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b c d e "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A051890 (2*(n^2 - n + 1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A319560 (Number of non-isomorphic strict T_0 multiset partitions of weight n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A028916 (Friedlander-Iwaniec primes: Primes of form a^2 + b^4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A057732 (Numbers k such that 2^k + 3 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A046376 (Palindromes with exactly 2 palindromic prime factors (counted with multiplicity), and no other prime factors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A002275 - OEIS". oeis.org. Retrieved 8 March 2024.
- ^ Sloane, N. J. A. (ed.). "Sequence A128455 (Numbers k such that 9^k - 2 is a prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A000009 (Expansion of Product_{m > 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A318949 (Number of ways to write n as an orderless product of orderless sums)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A038499 (Number of partitions of n into a prime number of parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A006748 (Number of diagonally symmetric polyominoes with n cells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A210000 (Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
- ^ Sloane, N. J. A. (ed.). "Sequence A033995 (Number of bipartite graphs with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A062801 (Number of 2 X 2 non-singular integer matrices with entries from {0,...,n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A000096 (n*(n+3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A057809 (Numbers n such that pi(n) divides n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 23 May 2024.
- ^ Van Ekeren, Jethro; Lam, Ching Hung; Möller, Sven; Shimakura, Hiroki (2021). "Schellekens' list and the very strange formula". Advances in Mathematics. 380. Amsterdam: Elsevier: 1–34 (107567). arXiv:2005.12248. doi:10.1016/j.aim.2021.107567. MR 4200469. S2CID 218870375. Zbl 1492.17027.
- ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005380". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A051026 (Number of primitive subsequences of 1, 2, ..., n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A080040 (2*a(n-1) + 2*a(n-2) for n > 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A264237 (Sum of values of vertices at level n of the hyperbolic Pascal pyramid)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A033991 (n*(4*n-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A006315 (Numbers n such that n^32 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A185982 (Triangle read by rows: number of set partitions of n elements with k connectors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A007534 (Even numbers that are not the sum of a pair of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A050993 (5-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006094 (Products of 2 successive primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A046368 (Products of two palindromic primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "1150 (number)". The encyclopedia of numbers.
- ^ a b "Sloane's A000101 : Increasing gaps between primes (upper end)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 July 2016.
- ^ a b "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b c d "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ "Sloane's A069125 : a(n) = (11*n^2 - 11*n + 2)/2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ "1157 (number)". The encyclopedia of numbers.
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A055887 (Number of ordered partitions of partitions)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A018805". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A024816 (Antisigma(n): Sum of the numbers less than n that do not divide n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A063776 - OEIS". oeis.org.
- ^ "A000256 - OEIS". oeis.org.
- ^ "1179 (number)". The encyclopedia of numbers.
- ^ "A000339 - OEIS". oeis.org.
- ^ "A271269 - OEIS". oeis.org.
- ^ "A000031 - OEIS". oeis.org.
- ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A051424 (Number of partitions of n into pairwise relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ "A121038 - OEIS". oeis.org.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A005449 (Second pentagonal numbers: n*(3*n + 1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A175654 - OEIS". oeis.org.
- ^ oeis.org/A062092
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A024916 (Sum_1^n sigma(k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e >Sloane, N. J. A. (ed.). "Sequence A080663 (3*n^2 - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Meehan, Eileen R., Why TV is not our fault: television programming, viewers, and who's really in control Lanham, MD: Rowman & Littlefield, 2005
- ^ "A265070 - OEIS". oeis.org.
- ^ "1204 (number)". The encyclopedia of numbers.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A240574 (Number of partitions of n such that the number of odd parts is a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A303815 - OEIS". oeis.org.
- ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A098237 (Composite de Polignac numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A337070 (Number of strict chains of divisors starting with the superprimorial A006939(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Higgins, ibid.
- ^ Sloane, N. J. A. (ed.). "Sequence A000070 (Sum_{0..n} A000041(k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A006355 (Number of binary vectors of length n containing no singletons)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A001110 : Square triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b c d e "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A303815 (Generalized 29-gonal (or icosienneagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A249911 (60-gonal (hexacontagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A004111 - OEIS". oeis.org.
- ^ "A061262 - OEIS". oeis.org.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A008302 (Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product{0..n-1} (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). Also enumerates permutations by their major index)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A006154 - OEIS". oeis.org.
- ^ "A000045 - OEIS". oeis.org.
- ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A160160 - OEIS". oeis.org.
- ^ "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A126796 (Number of complete partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ oeis.org/A305843
- ^ "A007690 - OEIS". oeis.org.
- ^ "Sloane's A033819 : Trimorphic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A058331 (2*n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A144300 (Number of partitions of n minus number of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000837 (Number of partitions of n into relatively prime parts. Also aperiodic partitions.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A193757 (Numbers which can be written with their digits in order and using only a plus and a squaring operator)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b c d e "Sloane's A014575 : Vampire numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A070169 (Rounded total surface area of a regular tetrahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A003238 (Number of rooted trees with n vertices in which vertices at the same level have the same degree)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A023894 (Number of partitions of n into prime power parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A072895 (Least k for the Theodorus spiral to complete n revolutions)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A100040 (2*n^2 + n - 5)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A051349 (Sum of first n nonprimes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A033286 (n * prime(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A084849 (1 + n + 2*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000930 (Narayana's cows sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001792 ((n+2)*2^(n-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A216492 (Number of inequivalent connected planar figures that can be formed from n 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007318 (Pascal's triangle read by rows)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014574 (Average of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A173831 (Largest prime < n^4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006872 (Numbers k such that phi(k) equals phi(sigma(k)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014285 (Sum_{1..n} j*prime(j))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A071400 (Rounded volume of a regular octahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A003114 (Number of partitions of n into parts 5k+1 or 5k+4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A033548 (Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000055 (Number of trees with n unlabeled nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A124826 - OEIS". oeis.org.
- ^ "A142005 - OEIS". oeis.org.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A338470 (Number of integer partitions of n with no part dividing all the others)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A066186 - OEIS". oeis.org.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A304716 (Number of integer partitions of n whose distinct parts are connected)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A115073 - OEIS". oeis.org.
- ^ "A061256 - OEIS". oeis.org.
- ^ "A061954 - OEIS". oeis.org.
- ^ Sloane, N. J. A. (ed.). "Sequence A057465 (Numbers k such that k^512 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A030299 - OEIS". oeis.org.
- ^ a b "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A005894 (Centered tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A018806 (Sum of gcd(x, y))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A018227 (Magic numbers: atoms with full shells containing any of these numbers of electrons are considered electronically stable)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A005064 - OEIS". oeis.org.
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A090781 (Numbers that can be expressed as the difference of the squares of primes in just one distinct way)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A056809 (Numbers k such that k, k+1 and k+2 are products of two primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A316473 - OEIS". oeis.org.
- ^ "A000032 - OEIS". oeis.org.
- ^ "1348 (number)". The encyclopedia of numbers.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A101624 (Stern-Jacobsthal number)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A064228 (From Recamán's sequence (A005132): values of n achieving records in A057167)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A057167 (Term in Recamán's sequence A005132 where n appears for first time, or -1 if n never appears)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A064227 (From Recamán's sequence (A005132): record values in A057167)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A000603". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000960 (Flavius Josephus's sieve: Start with the natural numbers; at the k-th sieving step, remove every (k+1)-st term of the sequence remaining after the (k-1)-st sieving step; iterate)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A330224 (Number of achiral integer partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001610 (a(n-1) + a(n-2) + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000032 (Lucas numbers: L(n-1) + L(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A005578 (Arima sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A001157 (sigma_2(n): sum of squares of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A005945 (Number of n-step mappings with 4 inputs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A001631 - OEIS". oeis.org. Retrieved 25 June 2023.
- ^ Sloane, N. J. A. (ed.). "Sequence A088274 (Numbers k such that 10^k + 7 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000111 (Euler or up/down numbers: e.g.f. sec(x) + tan(x))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002414 (Octagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A001567 : Fermat pseudoprimes to base 2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ "Sloane's A050217 : Super-Poulet numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A054552 (4*n^2 - 3*n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A017919 (Powers of sqrt(5) rounded down)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A109308 (Lesser emirps (primes whose digit reversal is a larger prime))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A007865 (Number of sum-free subsets of {1, ..., n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
- ^ a b Sloane, N. J. A. (ed.). "Sequence A325349 (Number of integer partitions of n whose augmented differences are distinct)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000060 (Number of signed trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A051400 (Smallest value of x such that M(x) equals n, where M() is Mertens's function A002321)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000682 : Semimeanders". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A002445 (Denominators of Bernoulli numbers B_{2n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A045918 (Describe n. Also called the "Say What You See" or "Look and Say" sequence LS(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A050710 (Smallest composite that when added to sum of prime factors reaches a prime after n iterations)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A067538 (Number of partitions of n in which the number of parts divides n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A051015 : Zeisel numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A059845 (n*(3*n + 11)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000097 (Number of partitions of n if there are two kinds of 1's and two kinds of 2's)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A061068 (Primes which are the sum of a prime and its subscript)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001359 (Lesser of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001764 (binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A071399 (Rounded volume of a regular tetrahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A006832 (Discriminants of totally real cubic fields)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A003037 (Smallest number of complexity n: smallest number requiring n 1's to build using +, * and ^)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005259 (Apery (Apéry) numbers: Sum_0^n (binomial(n,k)*binomial(n+k,k))^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A062325 (Numbers k for which phi(prime(k)) is a square)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A011379 (n^2*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A005918 (Number of points on surface of square pyramid: 3*n^2 + 2 (n>0))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A011257 (Geometric mean of phi(n) and sigma(n) is an integer)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007678 (Number of regions in regular n-gon with all diagonals drawn)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A056220 (2*n^2 - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A028569 (n*(n + 9))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A071398 (Rounded total surface area of a regular icosahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A085831 (Sum_1^{2^n} d(k) where d(k) is the number of divisors of k (A000005))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A064410 (Number of partitions of n with zero crank)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A075207 (Number of polyhexes with n cells that tile the plane by translation)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A015128 (Number of overpartitions of n: an overpartition of n is an ordered sequence of nonincreasing integers that sum to n, where the first occurrence of each integer may be overlined)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006578 (Triangular numbers plus quarter squares: n*(n+1)/2 + floor(n^2/4) (i.e., A000217(n) + A002620(n)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A098859 (Number of partitions of n into parts each of which is used a different number of times)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A307958 (Coreful perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A097979 (Total number of largest parts in all compositions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006330 (Number of corners, or planar partitions of n with only one row and one column)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A114411 (Triple primorial n###)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A034296 (Number of flat partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A084647 (Hypotenuses for which there exist exactly 3 distinct integer triangles)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A002071 (Number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most the n-th prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A325325 (Number of integer partitions of n with distinct differences between successive parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A325858 (Number of Golomb partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A018000 (Powers of cube root of 9 rounded down)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A062198 (Sum of first n semiprimes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A038147 (Number of polyhexes with n cells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000702 (number of conjugacy classes in the alternating group A_n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001970 (Functional determinants; partitions of partitions; Euler transform applied twice to all 1's sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A071396 (Rounded total surface area of a regular octahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000084 (Number of series-parallel networks with n unlabeled edges. Also called yoke-chains by Cayley and MacMahon)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000615 (Threshold functions of exactly n variables)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A100129 (Numbers k such that 2^k starts with k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000057 (Primes dividing all Fibonacci sequences)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A319066 (Number of partitions of integer partitions of n where all parts have the same length)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A056327 (Number of reversible string structures with n beads using exactly three different colors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002720 (Number of partial permutations of an n-set; number of n X n binary matrices with at most one 1 in each row and column)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A065381 (Primes not of the form p + 2^k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A140090 (n*(3*n + 7)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A169942 (Number of Golomb rulers of length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A169952 (Second entry in row n of triangle in A169950)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A034962 (Primes that are the sum of three consecutive primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A046386 (Products of four distinct primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A127106 (Numbers n such that n^2 divides 6^n-1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A008406 (Triangle T(n,k) read by rows, giving number of graphs with n nodes and k edges))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A057660 (Sum_{1..n} n/gcd(n,k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A088319 (Ordered hypotenuses of primitive Pythagorean triangles having legs that add up to a square)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A052486 (Achilles numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A056995 (Numbers k such that k^256 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A005231 : Odd abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A056026 (Numbers k such that k^14 is congruent with 1 (mod 15^2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A076409 (Sum of the quadratic residues of prime(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A070142 (Numbers n such that [A070080(n), A070081(n), A070082(n)] is an integer triangle with integer area)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A033428 (3*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A071402 (Rounded volume of a regular icosahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A326123 (a(n) is the sum of all divisors of the first n odd numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006327 (Fibonacci(n) - 3. Number of total preorders)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A100145 (Structured great rhombicosidodecahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A064174 (Number of partitions of n with nonnegative rank)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A023360 (Number of compositions of n into prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A103473 (Number of polyominoes consisting of 7 regular unit n-gons)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007584 (9-gonal (or enneagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A022004 (Initial members of prime triples (p, p+2, p+6))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006489 (Numbers k such that k-6, k, and k+6 are primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A213427 (Number of ways of refining the partition n^1 to get 1^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A134602 (Composite numbers such that the square mean of their prime factors is a nonprime integer (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A084990 (n*(n^2+3*n-1)/3)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A077068 (Semiprimes of the form prime + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A115160 (Numbers that are not the sum of two triangular numbers and a fourth power)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A046092 (4 times triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005382 (Primes p such that 2p-1 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001339 (Sum_{0..n} (k+1)! binomial(n,k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007290 (2*binomial(n,3))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A058360 (Number of partitions of n whose reciprocal sum is an integer)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A046931 (Prime islands: least prime whose adjacent primes are exactly 2n apart)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A056613 (Number of n-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A068140 (Smaller of two consecutive numbers each divisible by a cube greater than one)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A030272 (Number of partitions of n^3 into distinct cubes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A018818 (Number of partitions of n into divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A071401 (Rounded volume of a regular dodecahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A059802 (Numbers k such that 5^k - 4^k is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A082982 (Numbers k such that k, k+1 and k+2 are sums of 2 squares)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A057562 (Number of partitions of n into parts all relatively prime to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000230 (smallest prime p such that there is a gap of exactly 2n between p and next prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A261983 (Number of compositions of n such that at least two adjacent parts are equal)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A053781 (Numbers k that divide the sum of the first k composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A140480 (RMS numbers: numbers n such that root mean square of divisors of n is an integer)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A023108 (Positive integers which apparently never result in a palindrome under repeated applications of the function A056964(x))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A286518 (Number of finite connected sets of positive integers greater than one with least common multiple n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A004041 (Scaled sums of odd reciprocals: (2*n + 1)!!*(Sum_{0..n} 1/(2*k + 1)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A023359 (Number of compositions (ordered partitions) of n into powers of 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000787 (Strobogrammatic numbers: the same upside down)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A224930 (Numbers n such that n divides the concatenation of all divisors in descending order)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A294286 (Sum of the squares of the parts in the partitions of n into two distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A020989 ((5*4^n - 2)/3)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A331378 (Numbers whose product of prime indices is divisible by their sum of prime factors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A301700 (Number of aperiodic rooted trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A331452 (number of regions (or cells) formed by drawing the line segments connecting any two of the 2*(m+n) perimeter points of an m X n grid of squares)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A056045 ("Sum_{d divides n}(binomial(n,d))")". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A007850 : Giuga numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A161757 ((prime(n))^2 - (nonprime(n))^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A078374 (Number of partitions of n into distinct and relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A167008 (Sum_{0..n} C(n,k)^k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A033581 (6*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A350507 (Number of (not necessarily connected) unit-distance graphs on n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A102627 (Number of partitions of n into distinct parts in which the number of parts divides n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A216955 (number of binary sequences of length n and curling number k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001523 (Number of stacks, or planar partitions of n; also weakly unimodal compositions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A065764 (Sum of divisors of square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A220881 (Number of nonequivalent dissections of an n-gon into n-3 polygons by nonintersecting diagonals up to rotation)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A154964 (3*a(n-1) + 6*a(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A055327 (Triangle of rooted identity trees with n nodes and k leaves)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A316322 (Sum of piles of first n primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A045944 (Rhombic matchstick numbers: n*(3*n+2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A127816 (least k such that the remainder when 6^k is divided by k is n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005317 ((2^n + C(2*n,n))/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A064118 (Numbers k such that the first k digits of e form a prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A325860 (Number of subsets of {1..n} such that every pair of distinct elements has a different quotient)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A073592 (Euler transform of negative integers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A025047 (Alternating compositions, i.e., compositions with alternating increases and decreases, starting with either an increase or a decrease)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A288253 (Number of heptagons that can be formed with perimeter n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A235488 (Squarefree numbers which yield zero when their prime factors are xored together)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A075213 (Number of polyhexes with n cells that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A054377 : Primary pseudoperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Kellner, Bernard C.; 'The equation denom(Bn) = n has only one solution'
- ^ Sloane, N. J. A. (ed.). "Sequence A006318 (Large Schröder numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 May 2016.
- ^ "Sloane's A000058 : Sylvester's sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A083186 (Sum of first n primes whose indices are primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005260 (Sum_{0..n} binomial(n,k)^4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A056877 (Number of polyominoes with n cells, symmetric about two orthogonal axes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A061801 ((7*6^n - 2)/5)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A152927 (Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 4-gonal polygonal components chained with string components of length 1 as k varies)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A037032 (Total number of prime parts in all partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A101301 (The sum of the first n primes, minus n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
- ^ Sloane, N. J. A. (ed.). "Sequence A000230 (smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A004068 (Number of atoms in a decahedron with n shells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001905 (From higher-order Bernoulli numbers: absolute value of numerator of D-number D2n(2n-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A214083 (floor(n!^(1/3)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001208 (solution to the postage stamp problem with 3 denominations and n stamps)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000081 (Number of unlabeled rooted trees with n nodes (or connected functions with a fixed point))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A039771 (Numbers k such that phi(k) is a perfect cube)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A024026 (3^n - n^3)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A235945 (Number of partitions of n containing at least one prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A354493 (Number of quantales on n elements, up to isomorphism)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A088144 (Sum of primitive roots of n-th prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000166 (Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000240 (Rencontres numbers: number of permutations of [n] with exactly one fixed point)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000602 (Number of n-node unrooted quartic trees; number of n-carbon alkanes C(n)H(2n+2) ignoring stereoisomers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ ""Aztec Diamond"". Retrieved 20 September 2022.
- ^ Sloane, N. J. A. (ed.). "Sequence A082671 (Numbers n such that (n!-2)/2 is a prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A023811 (Largest metadrome (number with digits in strict ascending order) in base n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000990 (Number of plane partitions of n with at most two rows)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A164652 (Hultman numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007530 (Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A057568 (Number of partitions of n where n divides the product of the parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A011757 (prime(n^2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A004799 (Self convolution of Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005920 (Tricapped prism numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000609 (Number of threshold functions of n or fewer variables)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A259793 (Number of partitions of n^4 into fourth powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002998 (Smallest multiple of n whose digits sum to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005987 (Number of symmetric plane partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A023431 (Generalized Catalan Numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A217135 (Numbers n such that 3^n - 8 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A034897 : Hyperperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A240736 (Number of compositions of n having exactly one fixed point)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007070 (4*a(n-1) - 2*a(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000412 (Number of bipartite partitions of n white objects and 3 black ones)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A027851 (Number of nonisomorphic semigroups of order n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003060 (Smallest number with reciprocal of period length n in decimal (base 10))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A008514 (4-dimensional centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A024012 (2^n - n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002845 (Number of distinct values taken by 2^2^...^2 (with n 2's and parentheses inserted in all possible ways))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A051870 : 18-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A045648 (Number of chiral n-ominoes in (n-1)-space, one cell labeled)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000127 (Maximal number of regions obtained by joining n points around a circle by straight lines. Also number of regions in 4-space formed by n-1 hyperplanes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A178084 (Numbers k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A007419 (Largest number not the sum of distinct n-th-order polygonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A100953 (Number of partitions of n into relatively prime parts such that multiplicities of parts are also relatively prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A226366 (Numbers k such that 5*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A319014 (1*2*3 + 4*5*6 + 7*8*9 + 10*11*12 + 13*14*15 + 16*17*18 + ... + (up to n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A055621 (Number of covers of an unlabeled n-set)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000522 (Total number of ordered k-tuples of distinct elements from an n-element set)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A104621 (Heptanacci-Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005449 (Second pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002982 (Numbers n such that n! - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A030238 (Backwards shallow diagonal sums of Catalan triangle A009766)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A089046 (Least edge-length of a square dissectable into at least n squares in the Mrs. Perkins's quilt problem)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A065900 (Numbers n such that sigma(n) equals sigma(n-1) + sigma(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Jon Froemke & Jerrold W. Grossman (February 1993). "A Mod-n Ackermann Function, or What's So Special About 1969?". The American Mathematical Monthly. 100 (2). Mathematical Association of America: 180–183. doi:10.2307/2323780. JSTOR 2323780.
- ^ Sloane, N. J. A. (ed.). "Sequence A052542 (2*a(n-1) + a(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A024069 (6^n - n^7)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A217076 (Numbers n such that (n^37-1)/(n-1) is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A302545 (Number of non-isomorphic multiset partitions of weight n with no singletons)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A277288 (Positive integers n such that n divides (3^n + 5))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A187220 (Gullwing sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A046351 (Palindromic composite numbers with only palindromic prime factors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000612 (Number of P-equivalence classes of switching functions of n or fewer variables, divided by 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ OEIS: A059801
- ^ Sloane, N. J. A. (ed.). "Sequence A002470 (Glaisher's function W(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A263341 (Triangle read by rows: T(n,k) is the number of unlabeled graphs on n vertices with independence number k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A089085 (Numbers k such that (k! + 3)/3 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A011755 (Sum_{1..n} k*phi(k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.,
- ^ Sloane, N. J. A. (ed.). "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.