COOKIE CONSENT: By continuing to browse my site you agree to its use of cookies. OK or Tell me more
Search a number
octagonal numbers
A figurate number of form n(3n-2). more

The first 600 octagonal numbers :
1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, 408, 481, 560, 645, 736, 833, 936, 1045, 1160, 1281, 1408, 1541, 1680, 1825, 1976, 2133, 2296, 2465, 2640, 2821, 3008, 3201, 3400, 3605, 3816, 4033, 4256, 4485, 4720, 4961, 5208, 5461, 5720, 5985, 6256, 6533, 6816, 7105, 7400, 7701, 8008, 8321, 8640, 8965, 9296, 9633, 9976, 10325, 10680, 11041, 11408, 11781, 12160, 12545, 12936, 13333, 13736, 14145, 14560, 14981, 15408, 15841, 16280, 16725, 17176, 17633, 18096, 18565, 19040, 19521, 20008, 20501, 21000, 21505, 22016, 22533, 23056, 23585, 24120, 24661, 25208, 25761, 26320, 26885, 27456, 28033, 28616, 29205, 29800, 30401, 31008, 31621, 32240, 32865, 33496, 34133, 34776, 35425, 36080, 36741, 37408, 38081, 38760, 39445, 40136, 40833, 41536, 42245, 42960, 43681, 44408, 45141, 45880, 46625, 47376, 48133, 48896, 49665, 50440, 51221, 52008, 52801, 53600, 54405, 55216, 56033, 56856, 57685, 58520, 59361, 60208, 61061, 61920, 62785, 63656, 64533, 65416, 66305, 67200, 68101, 69008, 69921, 70840, 71765, 72696, 73633, 74576, 75525, 76480, 77441, 78408, 79381, 80360, 81345, 82336, 83333, 84336, 85345, 86360, 87381, 88408, 89441, 90480, 91525, 92576, 93633, 94696, 95765, 96840, 97921, 99008, 100101, 101200, 102305, 103416, 104533, 105656, 106785, 107920, 109061, 110208, 111361, 112520, 113685, 114856, 116033, 117216, 118405, 119600, 120801, 122008, 123221, 124440, 125665, 126896, 128133, 129376, 130625, 131880, 133141, 134408, 135681, 136960, 138245, 139536, 140833, 142136, 143445, 144760, 146081, 147408, 148741, 150080, 151425, 152776, 154133, 155496, 156865, 158240, 159621, 161008, 162401, 163800, 165205, 166616, 168033, 169456, 170885, 172320, 173761, 175208, 176661, 178120, 179585, 181056, 182533, 184016, 185505, 187000, 188501, 190008, 191521, 193040, 194565, 196096, 197633, 199176, 200725, 202280, 203841, 205408, 206981, 208560, 210145, 211736, 213333, 214936, 216545, 218160, 219781, 221408, 223041, 224680, 226325, 227976, 229633, 231296, 232965, 234640, 236321, 238008, 239701, 241400, 243105, 244816, 246533, 248256, 249985, 251720, 253461, 255208, 256961, 258720, 260485, 262256, 264033, 265816, 267605, 269400, 271201, 273008, 274821, 276640, 278465, 280296, 282133, 283976, 285825, 287680, 289541, 291408, 293281, 295160, 297045, 298936, 300833, 302736, 304645, 306560, 308481, 310408, 312341, 314280, 316225, 318176, 320133, 322096, 324065, 326040, 328021, 330008, 332001, 334000, 336005, 338016, 340033, 342056, 344085, 346120, 348161, 350208, 352261, 354320, 356385, 358456, 360533, 362616, 364705, 366800, 368901, 371008, 373121, 375240, 377365, 379496, 381633, 383776, 385925, 388080, 390241, 392408, 394581, 396760, 398945, 401136, 403333, 405536, 407745, 409960, 412181, 414408, 416641, 418880, 421125, 423376, 425633, 427896, 430165, 432440, 434721, 437008, 439301, 441600, 443905, 446216, 448533, 450856, 453185, 455520, 457861, 460208, 462561, 464920, 467285, 469656, 472033, 474416, 476805, 479200, 481601, 484008, 486421, 488840, 491265, 493696, 496133, 498576, 501025, 503480, 505941, 508408, 510881, 513360, 515845, 518336, 520833, 523336, 525845, 528360, 530881, 533408, 535941, 538480, 541025, 543576, 546133, 548696, 551265, 553840, 556421, 559008, 561601, 564200, 566805, 569416, 572033, 574656, 577285, 579920, 582561, 585208, 587861, 590520, 593185, 595856, 598533, 601216, 603905, 606600, 609301, 612008, 614721, 617440, 620165, 622896, 625633, 628376, 631125, 633880, 636641, 639408, 642181, 644960, 647745, 650536, 653333, 656136, 658945, 661760, 664581, 667408, 670241, 673080, 675925, 678776, 681633, 684496, 687365, 690240, 693121, 696008, 698901, 701800, 704705, 707616, 710533, 713456, 716385, 719320, 722261, 725208, 728161, 731120, 734085, 737056, 740033, 743016, 746005, 749000, 752001, 755008, 758021, 761040, 764065, 767096, 770133, 773176, 776225, 779280, 782341, 785408, 788481, 791560, 794645, 797736, 800833, 803936, 807045, 810160, 813281, 816408, 819541, 822680, 825825, 828976, 832133, 835296, 838465, 841640, 844821, 848008, 851201, 854400, 857605, 860816, 864033, 867256, 870485, 873720, 876961, 880208, 883461, 886720, 889985, 893256, 896533, 899816, 903105, 906400, 909701, 913008, 916321, 919640, 922965, 926296, 929633, 932976, 936325, 939680, 943041, 946408, 949781, 953160, 956545, 959936, 963333, 966736, 970145, 973560, 976981, 980408, 983841, 987280, 990725, 994176, 997633, 1001096, 1004565, 1008040, 1011521, 1015008, 1018501, 1022000, 1025505, 1029016, 1032533, 1036056, 1039585, 1043120, 1046661, 1050208, 1053761, 1057320, 1060885, 1064456, 1068033, 1071616, 1075205, 1078800.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 18257418 values, from 1 to 999999899565336).

n\r 0  1 
291287099128709 2 
3608580660858066085806 3 
49128709912870900 4 
573029667302968036514840 5 
6304290330429033042903304290330429033042903 6 
75216405521640626082020052164050 7 
891287094564355000456435400 8 
9202860220286022028602202860220286022028602202860220286022028602 9 
103651483365148401825742036514833651484018257420 10 
1133195303319531000331953001659765331953103319531

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.