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centered pentagonal numbers
Figurate numbers of the form 5n(n-1)/2 + 1. more

The first 600 centered pentagonal numbers :
1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391, 456, 526, 601, 681, 766, 856, 951, 1051, 1156, 1266, 1381, 1501, 1626, 1756, 1891, 2031, 2176, 2326, 2481, 2641, 2806, 2976, 3151, 3331, 3516, 3706, 3901, 4101, 4306, 4516, 4731, 4951, 5176, 5406, 5641, 5881, 6126, 6376, 6631, 6891, 7156, 7426, 7701, 7981, 8266, 8556, 8851, 9151, 9456, 9766, 10081, 10401, 10726, 11056, 11391, 11731, 12076, 12426, 12781, 13141, 13506, 13876, 14251, 14631, 15016, 15406, 15801, 16201, 16606, 17016, 17431, 17851, 18276, 18706, 19141, 19581, 20026, 20476, 20931, 21391, 21856, 22326, 22801, 23281, 23766, 24256, 24751, 25251, 25756, 26266, 26781, 27301, 27826, 28356, 28891, 29431, 29976, 30526, 31081, 31641, 32206, 32776, 33351, 33931, 34516, 35106, 35701, 36301, 36906, 37516, 38131, 38751, 39376, 40006, 40641, 41281, 41926, 42576, 43231, 43891, 44556, 45226, 45901, 46581, 47266, 47956, 48651, 49351, 50056, 50766, 51481, 52201, 52926, 53656, 54391, 55131, 55876, 56626, 57381, 58141, 58906, 59676, 60451, 61231, 62016, 62806, 63601, 64401, 65206, 66016, 66831, 67651, 68476, 69306, 70141, 70981, 71826, 72676, 73531, 74391, 75256, 76126, 77001, 77881, 78766, 79656, 80551, 81451, 82356, 83266, 84181, 85101, 86026, 86956, 87891, 88831, 89776, 90726, 91681, 92641, 93606, 94576, 95551, 96531, 97516, 98506, 99501, 100501, 101506, 102516, 103531, 104551, 105576, 106606, 107641, 108681, 109726, 110776, 111831, 112891, 113956, 115026, 116101, 117181, 118266, 119356, 120451, 121551, 122656, 123766, 124881, 126001, 127126, 128256, 129391, 130531, 131676, 132826, 133981, 135141, 136306, 137476, 138651, 139831, 141016, 142206, 143401, 144601, 145806, 147016, 148231, 149451, 150676, 151906, 153141, 154381, 155626, 156876, 158131, 159391, 160656, 161926, 163201, 164481, 165766, 167056, 168351, 169651, 170956, 172266, 173581, 174901, 176226, 177556, 178891, 180231, 181576, 182926, 184281, 185641, 187006, 188376, 189751, 191131, 192516, 193906, 195301, 196701, 198106, 199516, 200931, 202351, 203776, 205206, 206641, 208081, 209526, 210976, 212431, 213891, 215356, 216826, 218301, 219781, 221266, 222756, 224251, 225751, 227256, 228766, 230281, 231801, 233326, 234856, 236391, 237931, 239476, 241026, 242581, 244141, 245706, 247276, 248851, 250431, 252016, 253606, 255201, 256801, 258406, 260016, 261631, 263251, 264876, 266506, 268141, 269781, 271426, 273076, 274731, 276391, 278056, 279726, 281401, 283081, 284766, 286456, 288151, 289851, 291556, 293266, 294981, 296701, 298426, 300156, 301891, 303631, 305376, 307126, 308881, 310641, 312406, 314176, 315951, 317731, 319516, 321306, 323101, 324901, 326706, 328516, 330331, 332151, 333976, 335806, 337641, 339481, 341326, 343176, 345031, 346891, 348756, 350626, 352501, 354381, 356266, 358156, 360051, 361951, 363856, 365766, 367681, 369601, 371526, 373456, 375391, 377331, 379276, 381226, 383181, 385141, 387106, 389076, 391051, 393031, 395016, 397006, 399001, 401001, 403006, 405016, 407031, 409051, 411076, 413106, 415141, 417181, 419226, 421276, 423331, 425391, 427456, 429526, 431601, 433681, 435766, 437856, 439951, 442051, 444156, 446266, 448381, 450501, 452626, 454756, 456891, 459031, 461176, 463326, 465481, 467641, 469806, 471976, 474151, 476331, 478516, 480706, 482901, 485101, 487306, 489516, 491731, 493951, 496176, 498406, 500641, 502881, 505126, 507376, 509631, 511891, 514156, 516426, 518701, 520981, 523266, 525556, 527851, 530151, 532456, 534766, 537081, 539401, 541726, 544056, 546391, 548731, 551076, 553426, 555781, 558141, 560506, 562876, 565251, 567631, 570016, 572406, 574801, 577201, 579606, 582016, 584431, 586851, 589276, 591706, 594141, 596581, 599026, 601476, 603931, 606391, 608856, 611326, 613801, 616281, 618766, 621256, 623751, 626251, 628756, 631266, 633781, 636301, 638826, 641356, 643891, 646431, 648976, 651526, 654081, 656641, 659206, 661776, 664351, 666931, 669516, 672106, 674701, 677301, 679906, 682516, 685131, 687751, 690376, 693006, 695641, 698281, 700926, 703576, 706231, 708891, 711556, 714226, 716901, 719581, 722266, 724956, 727651, 730351, 733056, 735766, 738481, 741201, 743926, 746656, 749391, 752131, 754876, 757626, 760381, 763141, 765906, 768676, 771451, 774231, 777016, 779806, 782601, 785401, 788206, 791016, 793831, 796651, 799476, 802306, 805141, 807981, 810826, 813676, 816531, 819391, 822256, 825126, 828001, 830881, 833766, 836656, 839551, 842451, 845356, 848266, 851181, 854101, 857026, 859956, 862891, 865831, 868776, 871726, 874681, 877641, 880606, 883576, 886551, 889531, 892516, 895506, 898501.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 20000000 values, from 1 to 999999950000001).

n\r 0  1 
21000000010000000 2 
36666667133333330 3 
45000000500000050000005000000 4 
5020000000000 5 
6333333366666660333333466666670 6 
70571428557142862857143005714286 7 
825000002500000250000025000002500000250000025000002500000 8 
9044444450044444440666666744444440 9 
10010000000000010000000000 10 
1103636363000363636436363633636364036363641818182

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.