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centered nonagonal numbers
Figurate numbers of the form 9n(n-1)/2 + 1. more

The first 600 centered nonagonal numbers :
1, 10, 28, 55, 91, 136, 190, 253, 325, 406, 496, 595, 703, 820, 946, 1081, 1225, 1378, 1540, 1711, 1891, 2080, 2278, 2485, 2701, 2926, 3160, 3403, 3655, 3916, 4186, 4465, 4753, 5050, 5356, 5671, 5995, 6328, 6670, 7021, 7381, 7750, 8128, 8515, 8911, 9316, 9730, 10153, 10585, 11026, 11476, 11935, 12403, 12880, 13366, 13861, 14365, 14878, 15400, 15931, 16471, 17020, 17578, 18145, 18721, 19306, 19900, 20503, 21115, 21736, 22366, 23005, 23653, 24310, 24976, 25651, 26335, 27028, 27730, 28441, 29161, 29890, 30628, 31375, 32131, 32896, 33670, 34453, 35245, 36046, 36856, 37675, 38503, 39340, 40186, 41041, 41905, 42778, 43660, 44551, 45451, 46360, 47278, 48205, 49141, 50086, 51040, 52003, 52975, 53956, 54946, 55945, 56953, 57970, 58996, 60031, 61075, 62128, 63190, 64261, 65341, 66430, 67528, 68635, 69751, 70876, 72010, 73153, 74305, 75466, 76636, 77815, 79003, 80200, 81406, 82621, 83845, 85078, 86320, 87571, 88831, 90100, 91378, 92665, 93961, 95266, 96580, 97903, 99235, 100576, 101926, 103285, 104653, 106030, 107416, 108811, 110215, 111628, 113050, 114481, 115921, 117370, 118828, 120295, 121771, 123256, 124750, 126253, 127765, 129286, 130816, 132355, 133903, 135460, 137026, 138601, 140185, 141778, 143380, 144991, 146611, 148240, 149878, 151525, 153181, 154846, 156520, 158203, 159895, 161596, 163306, 165025, 166753, 168490, 170236, 171991, 173755, 175528, 177310, 179101, 180901, 182710, 184528, 186355, 188191, 190036, 191890, 193753, 195625, 197506, 199396, 201295, 203203, 205120, 207046, 208981, 210925, 212878, 214840, 216811, 218791, 220780, 222778, 224785, 226801, 228826, 230860, 232903, 234955, 237016, 239086, 241165, 243253, 245350, 247456, 249571, 251695, 253828, 255970, 258121, 260281, 262450, 264628, 266815, 269011, 271216, 273430, 275653, 277885, 280126, 282376, 284635, 286903, 289180, 291466, 293761, 296065, 298378, 300700, 303031, 305371, 307720, 310078, 312445, 314821, 317206, 319600, 322003, 324415, 326836, 329266, 331705, 334153, 336610, 339076, 341551, 344035, 346528, 349030, 351541, 354061, 356590, 359128, 361675, 364231, 366796, 369370, 371953, 374545, 377146, 379756, 382375, 385003, 387640, 390286, 392941, 395605, 398278, 400960, 403651, 406351, 409060, 411778, 414505, 417241, 419986, 422740, 425503, 428275, 431056, 433846, 436645, 439453, 442270, 445096, 447931, 450775, 453628, 456490, 459361, 462241, 465130, 468028, 470935, 473851, 476776, 479710, 482653, 485605, 488566, 491536, 494515, 497503, 500500, 503506, 506521, 509545, 512578, 515620, 518671, 521731, 524800, 527878, 530965, 534061, 537166, 540280, 543403, 546535, 549676, 552826, 555985, 559153, 562330, 565516, 568711, 571915, 575128, 578350, 581581, 584821, 588070, 591328, 594595, 597871, 601156, 604450, 607753, 611065, 614386, 617716, 621055, 624403, 627760, 631126, 634501, 637885, 641278, 644680, 648091, 651511, 654940, 658378, 661825, 665281, 668746, 672220, 675703, 679195, 682696, 686206, 689725, 693253, 696790, 700336, 703891, 707455, 711028, 714610, 718201, 721801, 725410, 729028, 732655, 736291, 739936, 743590, 747253, 750925, 754606, 758296, 761995, 765703, 769420, 773146, 776881, 780625, 784378, 788140, 791911, 795691, 799480, 803278, 807085, 810901, 814726, 818560, 822403, 826255, 830116, 833986, 837865, 841753, 845650, 849556, 853471, 857395, 861328, 865270, 869221, 873181, 877150, 881128, 885115, 889111, 893116, 897130, 901153, 905185, 909226, 913276, 917335, 921403, 925480, 929566, 933661, 937765, 941878, 946000, 950131, 954271, 958420, 962578, 966745, 970921, 975106, 979300, 983503, 987715, 991936, 996166, 1000405, 1004653, 1008910, 1013176, 1017451, 1021735, 1026028, 1030330, 1034641, 1038961, 1043290, 1047628, 1051975, 1056331, 1060696, 1065070, 1069453, 1073845, 1078246, 1082656, 1087075, 1091503, 1095940, 1100386, 1104841, 1109305, 1113778, 1118260, 1122751, 1127251, 1131760, 1136278, 1140805, 1145341, 1149886, 1154440, 1159003, 1163575, 1168156, 1172746, 1177345, 1181953, 1186570, 1191196, 1195831, 1200475, 1205128, 1209790, 1214461, 1219141, 1223830, 1228528, 1233235, 1237951, 1242676, 1247410, 1252153, 1256905, 1261666, 1266436, 1271215, 1276003, 1280800, 1285606, 1290421, 1295245, 1300078, 1304920, 1309771, 1314631, 1319500, 1324378, 1329265, 1334161, 1339066, 1343980, 1348903, 1353835, 1358776, 1363726, 1368685, 1373653, 1378630, 1383616, 1388611, 1393615, 1398628, 1403650, 1408681, 1413721, 1418770, 1423828, 1428895, 1433971, 1439056, 1444150, 1449253, 1454365, 1459486, 1464616, 1469755, 1474903, 1480060, 1485226, 1490401, 1495585, 1500778, 1505980, 1511191, 1516411, 1521640, 1526878, 1532125, 1537381, 1542646, 1547920, 1553203, 1558495, 1563796, 1569106, 1574425, 1579753, 1585090, 1590436, 1595791, 1601155, 1606528, 1611910, 1617301.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 14907120 values, from 1 to 999999953042761).

n\r 0  1 
274535607453560 2 
30149071200 3 
43726780372678037267803726780 4 
559628485962848029814240 5 
6074535600074535600 6 
74259177425917704259177002129589 7 
818633901863390186339018633901863390186339018633901863390 8 
90149071200000000 9 
102981424298142401490712029814242981424014907120 10 
1127103862710385027103861355193027103850002710385

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.