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centered heptagonal numbers
Figurate numbers of the form 7n(n-1)/2 + 1. more

The first 600 centered heptagonal numbers :
1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953, 1072, 1198, 1331, 1471, 1618, 1772, 1933, 2101, 2276, 2458, 2647, 2843, 3046, 3256, 3473, 3697, 3928, 4166, 4411, 4663, 4922, 5188, 5461, 5741, 6028, 6322, 6623, 6931, 7246, 7568, 7897, 8233, 8576, 8926, 9283, 9647, 10018, 10396, 10781, 11173, 11572, 11978, 12391, 12811, 13238, 13672, 14113, 14561, 15016, 15478, 15947, 16423, 16906, 17396, 17893, 18397, 18908, 19426, 19951, 20483, 21022, 21568, 22121, 22681, 23248, 23822, 24403, 24991, 25586, 26188, 26797, 27413, 28036, 28666, 29303, 29947, 30598, 31256, 31921, 32593, 33272, 33958, 34651, 35351, 36058, 36772, 37493, 38221, 38956, 39698, 40447, 41203, 41966, 42736, 43513, 44297, 45088, 45886, 46691, 47503, 48322, 49148, 49981, 50821, 51668, 52522, 53383, 54251, 55126, 56008, 56897, 57793, 58696, 59606, 60523, 61447, 62378, 63316, 64261, 65213, 66172, 67138, 68111, 69091, 70078, 71072, 72073, 73081, 74096, 75118, 76147, 77183, 78226, 79276, 80333, 81397, 82468, 83546, 84631, 85723, 86822, 87928, 89041, 90161, 91288, 92422, 93563, 94711, 95866, 97028, 98197, 99373, 100556, 101746, 102943, 104147, 105358, 106576, 107801, 109033, 110272, 111518, 112771, 114031, 115298, 116572, 117853, 119141, 120436, 121738, 123047, 124363, 125686, 127016, 128353, 129697, 131048, 132406, 133771, 135143, 136522, 137908, 139301, 140701, 142108, 143522, 144943, 146371, 147806, 149248, 150697, 152153, 153616, 155086, 156563, 158047, 159538, 161036, 162541, 164053, 165572, 167098, 168631, 170171, 171718, 173272, 174833, 176401, 177976, 179558, 181147, 182743, 184346, 185956, 187573, 189197, 190828, 192466, 194111, 195763, 197422, 199088, 200761, 202441, 204128, 205822, 207523, 209231, 210946, 212668, 214397, 216133, 217876, 219626, 221383, 223147, 224918, 226696, 228481, 230273, 232072, 233878, 235691, 237511, 239338, 241172, 243013, 244861, 246716, 248578, 250447, 252323, 254206, 256096, 257993, 259897, 261808, 263726, 265651, 267583, 269522, 271468, 273421, 275381, 277348, 279322, 281303, 283291, 285286, 287288, 289297, 291313, 293336, 295366, 297403, 299447, 301498, 303556, 305621, 307693, 309772, 311858, 313951, 316051, 318158, 320272, 322393, 324521, 326656, 328798, 330947, 333103, 335266, 337436, 339613, 341797, 343988, 346186, 348391, 350603, 352822, 355048, 357281, 359521, 361768, 364022, 366283, 368551, 370826, 373108, 375397, 377693, 379996, 382306, 384623, 386947, 389278, 391616, 393961, 396313, 398672, 401038, 403411, 405791, 408178, 410572, 412973, 415381, 417796, 420218, 422647, 425083, 427526, 429976, 432433, 434897, 437368, 439846, 442331, 444823, 447322, 449828, 452341, 454861, 457388, 459922, 462463, 465011, 467566, 470128, 472697, 475273, 477856, 480446, 483043, 485647, 488258, 490876, 493501, 496133, 498772, 501418, 504071, 506731, 509398, 512072, 514753, 517441, 520136, 522838, 525547, 528263, 530986, 533716, 536453, 539197, 541948, 544706, 547471, 550243, 553022, 555808, 558601, 561401, 564208, 567022, 569843, 572671, 575506, 578348, 581197, 584053, 586916, 589786, 592663, 595547, 598438, 601336, 604241, 607153, 610072, 612998, 615931, 618871, 621818, 624772, 627733, 630701, 633676, 636658, 639647, 642643, 645646, 648656, 651673, 654697, 657728, 660766, 663811, 666863, 669922, 672988, 676061, 679141, 682228, 685322, 688423, 691531, 694646, 697768, 700897, 704033, 707176, 710326, 713483, 716647, 719818, 722996, 726181, 729373, 732572, 735778, 738991, 742211, 745438, 748672, 751913, 755161, 758416, 761678, 764947, 768223, 771506, 774796, 778093, 781397, 784708, 788026, 791351, 794683, 798022, 801368, 804721, 808081, 811448, 814822, 818203, 821591, 824986, 828388, 831797, 835213, 838636, 842066, 845503, 848947, 852398, 855856, 859321, 862793, 866272, 869758, 873251, 876751, 880258, 883772, 887293, 890821, 894356, 897898, 901447, 905003, 908566, 912136, 915713, 919297, 922888, 926486, 930091, 933703, 937322, 940948, 944581, 948221, 951868, 955522, 959183, 962851, 966526, 970208, 973897, 977593, 981296, 985006, 988723, 992447, 996178, 999916, 1003661, 1007413, 1011172, 1014938, 1018711, 1022491, 1026278, 1030072, 1033873, 1037681, 1041496, 1045318, 1049147, 1052983, 1056826, 1060676, 1064533, 1068397, 1072268, 1076146, 1080031, 1083923, 1087822, 1091728, 1095641, 1099561, 1103488, 1107422, 1111363, 1115311, 1119266, 1123228, 1127197, 1131173, 1135156, 1139146, 1143143, 1147147, 1151158, 1155176, 1159201, 1163233, 1167272, 1171318, 1175371, 1179431, 1183498, 1187572, 1191653, 1195741, 1199836, 1203938, 1208047, 1212163, 1216286, 1220416, 1224553, 1228697, 1232848, 1237006, 1241171, 1245343, 1249522, 1253708, 1257901.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 16903085 values, from 1 to 999999929649491).

n\r 0  1 
284515428451543 2 
30112687235634362 3 
44225771422577142257714225772 4 
506761234338061767612340 5 
6056343622817181056343612817181 6 
701690308500000 7 
821128852112885211288621128862112886211288621128852112886 8 
9037562410037562410037562415634362 9 
100338061816903093380617003380616169030833806170 10 
1130732883073289000307328801536644307328803073288

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.