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decagonal numbers
Figurate numbers of the form n(4n-3). more

The first 600 decagonal numbers :
1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326, 8695, 9072, 9457, 9850, 10251, 10660, 11077, 11502, 11935, 12376, 12825, 13282, 13747, 14220, 14701, 15190, 15687, 16192, 16705, 17226, 17755, 18292, 18837, 19390, 19951, 20520, 21097, 21682, 22275, 22876, 23485, 24102, 24727, 25360, 26001, 26650, 27307, 27972, 28645, 29326, 30015, 30712, 31417, 32130, 32851, 33580, 34317, 35062, 35815, 36576, 37345, 38122, 38907, 39700, 40501, 41310, 42127, 42952, 43785, 44626, 45475, 46332, 47197, 48070, 48951, 49840, 50737, 51642, 52555, 53476, 54405, 55342, 56287, 57240, 58201, 59170, 60147, 61132, 62125, 63126, 64135, 65152, 66177, 67210, 68251, 69300, 70357, 71422, 72495, 73576, 74665, 75762, 76867, 77980, 79101, 80230, 81367, 82512, 83665, 84826, 85995, 87172, 88357, 89550, 90751, 91960, 93177, 94402, 95635, 96876, 98125, 99382, 100647, 101920, 103201, 104490, 105787, 107092, 108405, 109726, 111055, 112392, 113737, 115090, 116451, 117820, 119197, 120582, 121975, 123376, 124785, 126202, 127627, 129060, 130501, 131950, 133407, 134872, 136345, 137826, 139315, 140812, 142317, 143830, 145351, 146880, 148417, 149962, 151515, 153076, 154645, 156222, 157807, 159400, 161001, 162610, 164227, 165852, 167485, 169126, 170775, 172432, 174097, 175770, 177451, 179140, 180837, 182542, 184255, 185976, 187705, 189442, 191187, 192940, 194701, 196470, 198247, 200032, 201825, 203626, 205435, 207252, 209077, 210910, 212751, 214600, 216457, 218322, 220195, 222076, 223965, 225862, 227767, 229680, 231601, 233530, 235467, 237412, 239365, 241326, 243295, 245272, 247257, 249250, 251251, 253260, 255277, 257302, 259335, 261376, 263425, 265482, 267547, 269620, 271701, 273790, 275887, 277992, 280105, 282226, 284355, 286492, 288637, 290790, 292951, 295120, 297297, 299482, 301675, 303876, 306085, 308302, 310527, 312760, 315001, 317250, 319507, 321772, 324045, 326326, 328615, 330912, 333217, 335530, 337851, 340180, 342517, 344862, 347215, 349576, 351945, 354322, 356707, 359100, 361501, 363910, 366327, 368752, 371185, 373626, 376075, 378532, 380997, 383470, 385951, 388440, 390937, 393442, 395955, 398476, 401005, 403542, 406087, 408640, 411201, 413770, 416347, 418932, 421525, 424126, 426735, 429352, 431977, 434610, 437251, 439900, 442557, 445222, 447895, 450576, 453265, 455962, 458667, 461380, 464101, 466830, 469567, 472312, 475065, 477826, 480595, 483372, 486157, 488950, 491751, 494560, 497377, 500202, 503035, 505876, 508725, 511582, 514447, 517320, 520201, 523090, 525987, 528892, 531805, 534726, 537655, 540592, 543537, 546490, 549451, 552420, 555397, 558382, 561375, 564376, 567385, 570402, 573427, 576460, 579501, 582550, 585607, 588672, 591745, 594826, 597915, 601012, 604117, 607230, 610351, 613480, 616617, 619762, 622915, 626076, 629245, 632422, 635607, 638800, 642001, 645210, 648427, 651652, 654885, 658126, 661375, 664632, 667897, 671170, 674451, 677740, 681037, 684342, 687655, 690976, 694305, 697642, 700987, 704340, 707701, 711070, 714447, 717832, 721225, 724626, 728035, 731452, 734877, 738310, 741751, 745200, 748657, 752122, 755595, 759076, 762565, 766062, 769567, 773080, 776601, 780130, 783667, 787212, 790765, 794326, 797895, 801472, 805057, 808650, 812251, 815860, 819477, 823102, 826735, 830376, 834025, 837682, 841347, 845020, 848701, 852390, 856087, 859792, 863505, 867226, 870955, 874692, 878437, 882190, 885951, 889720, 893497, 897282, 901075, 904876, 908685, 912502, 916327, 920160, 924001, 927850, 931707, 935572, 939445, 943326, 947215, 951112, 955017, 958930, 962851, 966780, 970717, 974662, 978615, 982576, 986545, 990522, 994507, 998500, 1002501, 1006510, 1010527, 1014552, 1018585, 1022626, 1026675, 1030732, 1034797, 1038870, 1042951, 1047040, 1051137, 1055242, 1059355, 1063476, 1067605, 1071742, 1075887, 1080040, 1084201, 1088370, 1092547, 1096732, 1100925, 1105126, 1109335, 1113552, 1117777, 1122010, 1126251, 1130500, 1134757, 1139022, 1143295, 1147576, 1151865, 1156162, 1160467, 1164780, 1169101, 1173430, 1177767, 1182112, 1186465, 1190826, 1195195, 1199572, 1203957, 1208350, 1212751, 1217160, 1221577, 1226002, 1230435, 1234876, 1239325, 1243782, 1248247, 1252720, 1257201, 1261690, 1266187, 1270692, 1275205, 1279726, 1284255, 1288792, 1293337, 1297890, 1302451, 1307020, 1311597, 1316182, 1320775, 1325376, 1329985, 1334602, 1339227, 1343860, 1348501, 1353150, 1357807, 1362472, 1367145, 1371826, 1376515, 1381212, 1385917, 1390630, 1395351, 1400080, 1404817, 1409562, 1414315, 1419076, 1423845, 1428622, 1433407, 1438200.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 15811388 values, from 1 to 999999914512012).

n\r 0  1 
279056947905694 2 
35270462105409260 3 
43952847395284739528473952847 4 
563245553162278632455500 5 
6263523152704630263523152704630 6 
74517538451754004517540002258770 7 
819764231976424197642419764241976424197642319764231976423 8 
9527046235136420035136420035136420 9 
103162277158113931622780031622781581139316227700 10 
1128747972874798000287479801437399287479802874798

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.