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A figurate number of form 3n(n-1) + 1. more

The first 600 hex numbers :
1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919, 1027, 1141, 1261, 1387, 1519, 1657, 1801, 1951, 2107, 2269, 2437, 2611, 2791, 2977, 3169, 3367, 3571, 3781, 3997, 4219, 4447, 4681, 4921, 5167, 5419, 5677, 5941, 6211, 6487, 6769, 7057, 7351, 7651, 7957, 8269, 8587, 8911, 9241, 9577, 9919, 10267, 10621, 10981, 11347, 11719, 12097, 12481, 12871, 13267, 13669, 14077, 14491, 14911, 15337, 15769, 16207, 16651, 17101, 17557, 18019, 18487, 18961, 19441, 19927, 20419, 20917, 21421, 21931, 22447, 22969, 23497, 24031, 24571, 25117, 25669, 26227, 26791, 27361, 27937, 28519, 29107, 29701, 30301, 30907, 31519, 32137, 32761, 33391, 34027, 34669, 35317, 35971, 36631, 37297, 37969, 38647, 39331, 40021, 40717, 41419, 42127, 42841, 43561, 44287, 45019, 45757, 46501, 47251, 48007, 48769, 49537, 50311, 51091, 51877, 52669, 53467, 54271, 55081, 55897, 56719, 57547, 58381, 59221, 60067, 60919, 61777, 62641, 63511, 64387, 65269, 66157, 67051, 67951, 68857, 69769, 70687, 71611, 72541, 73477, 74419, 75367, 76321, 77281, 78247, 79219, 80197, 81181, 82171, 83167, 84169, 85177, 86191, 87211, 88237, 89269, 90307, 91351, 92401, 93457, 94519, 95587, 96661, 97741, 98827, 99919, 101017, 102121, 103231, 104347, 105469, 106597, 107731, 108871, 110017, 111169, 112327, 113491, 114661, 115837, 117019, 118207, 119401, 120601, 121807, 123019, 124237, 125461, 126691, 127927, 129169, 130417, 131671, 132931, 134197, 135469, 136747, 138031, 139321, 140617, 141919, 143227, 144541, 145861, 147187, 148519, 149857, 151201, 152551, 153907, 155269, 156637, 158011, 159391, 160777, 162169, 163567, 164971, 166381, 167797, 169219, 170647, 172081, 173521, 174967, 176419, 177877, 179341, 180811, 182287, 183769, 185257, 186751, 188251, 189757, 191269, 192787, 194311, 195841, 197377, 198919, 200467, 202021, 203581, 205147, 206719, 208297, 209881, 211471, 213067, 214669, 216277, 217891, 219511, 221137, 222769, 224407, 226051, 227701, 229357, 231019, 232687, 234361, 236041, 237727, 239419, 241117, 242821, 244531, 246247, 247969, 249697, 251431, 253171, 254917, 256669, 258427, 260191, 261961, 263737, 265519, 267307, 269101, 270901, 272707, 274519, 276337, 278161, 279991, 281827, 283669, 285517, 287371, 289231, 291097, 292969, 294847, 296731, 298621, 300517, 302419, 304327, 306241, 308161, 310087, 312019, 313957, 315901, 317851, 319807, 321769, 323737, 325711, 327691, 329677, 331669, 333667, 335671, 337681, 339697, 341719, 343747, 345781, 347821, 349867, 351919, 353977, 356041, 358111, 360187, 362269, 364357, 366451, 368551, 370657, 372769, 374887, 377011, 379141, 381277, 383419, 385567, 387721, 389881, 392047, 394219, 396397, 398581, 400771, 402967, 405169, 407377, 409591, 411811, 414037, 416269, 418507, 420751, 423001, 425257, 427519, 429787, 432061, 434341, 436627, 438919, 441217, 443521, 445831, 448147, 450469, 452797, 455131, 457471, 459817, 462169, 464527, 466891, 469261, 471637, 474019, 476407, 478801, 481201, 483607, 486019, 488437, 490861, 493291, 495727, 498169, 500617, 503071, 505531, 507997, 510469, 512947, 515431, 517921, 520417, 522919, 525427, 527941, 530461, 532987, 535519, 538057, 540601, 543151, 545707, 548269, 550837, 553411, 555991, 558577, 561169, 563767, 566371, 568981, 571597, 574219, 576847, 579481, 582121, 584767, 587419, 590077, 592741, 595411, 598087, 600769, 603457, 606151, 608851, 611557, 614269, 616987, 619711, 622441, 625177, 627919, 630667, 633421, 636181, 638947, 641719, 644497, 647281, 650071, 652867, 655669, 658477, 661291, 664111, 666937, 669769, 672607, 675451, 678301, 681157, 684019, 686887, 689761, 692641, 695527, 698419, 701317, 704221, 707131, 710047, 712969, 715897, 718831, 721771, 724717, 727669, 730627, 733591, 736561, 739537, 742519, 745507, 748501, 751501, 754507, 757519, 760537, 763561, 766591, 769627, 772669, 775717, 778771, 781831, 784897, 787969, 791047, 794131, 797221, 800317, 803419, 806527, 809641, 812761, 815887, 819019, 822157, 825301, 828451, 831607, 834769, 837937, 841111, 844291, 847477, 850669, 853867, 857071, 860281, 863497, 866719, 869947, 873181, 876421, 879667, 882919, 886177, 889441, 892711, 895987, 899269, 902557, 905851, 909151, 912457, 915769, 919087, 922411, 925741, 929077, 932419, 935767, 939121, 942481, 945847, 949219, 952597, 955981, 959371, 962767, 966169, 969577, 972991, 976411, 979837, 983269, 986707, 990151, 993601, 997057, 1000519, 1003987, 1007461, 1010941, 1014427, 1017919, 1021417, 1024921, 1028431, 1031947, 1035469, 1038997, 1042531, 1046071, 1049617, 1053169, 1056727, 1060291, 1063861, 1067437, 1071019, 1074607, 1078201.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 18257419 values, from 1 to 999999990852427).

n\r 0  1 
2018257419 2 
30182574190 3 
40912870909128710 4 
507302967730296803651484 5 
60182574190000 6 
75216405521640526082030052164060 7 
804564355045643550456435404564355 8 
90121716130000060858060 9 
100730296700000730296803651484 10 
1103319531016597653319531033195303319531331953100

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.