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star numbers
Figurate numbers of the form 6n(n-1) + 1. more

The first 600 star numbers :
1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, 1093, 1261, 1441, 1633, 1837, 2053, 2281, 2521, 2773, 3037, 3313, 3601, 3901, 4213, 4537, 4873, 5221, 5581, 5953, 6337, 6733, 7141, 7561, 7993, 8437, 8893, 9361, 9841, 10333, 10837, 11353, 11881, 12421, 12973, 13537, 14113, 14701, 15301, 15913, 16537, 17173, 17821, 18481, 19153, 19837, 20533, 21241, 21961, 22693, 23437, 24193, 24961, 25741, 26533, 27337, 28153, 28981, 29821, 30673, 31537, 32413, 33301, 34201, 35113, 36037, 36973, 37921, 38881, 39853, 40837, 41833, 42841, 43861, 44893, 45937, 46993, 48061, 49141, 50233, 51337, 52453, 53581, 54721, 55873, 57037, 58213, 59401, 60601, 61813, 63037, 64273, 65521, 66781, 68053, 69337, 70633, 71941, 73261, 74593, 75937, 77293, 78661, 80041, 81433, 82837, 84253, 85681, 87121, 88573, 90037, 91513, 93001, 94501, 96013, 97537, 99073, 100621, 102181, 103753, 105337, 106933, 108541, 110161, 111793, 113437, 115093, 116761, 118441, 120133, 121837, 123553, 125281, 127021, 128773, 130537, 132313, 134101, 135901, 137713, 139537, 141373, 143221, 145081, 146953, 148837, 150733, 152641, 154561, 156493, 158437, 160393, 162361, 164341, 166333, 168337, 170353, 172381, 174421, 176473, 178537, 180613, 182701, 184801, 186913, 189037, 191173, 193321, 195481, 197653, 199837, 202033, 204241, 206461, 208693, 210937, 213193, 215461, 217741, 220033, 222337, 224653, 226981, 229321, 231673, 234037, 236413, 238801, 241201, 243613, 246037, 248473, 250921, 253381, 255853, 258337, 260833, 263341, 265861, 268393, 270937, 273493, 276061, 278641, 281233, 283837, 286453, 289081, 291721, 294373, 297037, 299713, 302401, 305101, 307813, 310537, 313273, 316021, 318781, 321553, 324337, 327133, 329941, 332761, 335593, 338437, 341293, 344161, 347041, 349933, 352837, 355753, 358681, 361621, 364573, 367537, 370513, 373501, 376501, 379513, 382537, 385573, 388621, 391681, 394753, 397837, 400933, 404041, 407161, 410293, 413437, 416593, 419761, 422941, 426133, 429337, 432553, 435781, 439021, 442273, 445537, 448813, 452101, 455401, 458713, 462037, 465373, 468721, 472081, 475453, 478837, 482233, 485641, 489061, 492493, 495937, 499393, 502861, 506341, 509833, 513337, 516853, 520381, 523921, 527473, 531037, 534613, 538201, 541801, 545413, 549037, 552673, 556321, 559981, 563653, 567337, 571033, 574741, 578461, 582193, 585937, 589693, 593461, 597241, 601033, 604837, 608653, 612481, 616321, 620173, 624037, 627913, 631801, 635701, 639613, 643537, 647473, 651421, 655381, 659353, 663337, 667333, 671341, 675361, 679393, 683437, 687493, 691561, 695641, 699733, 703837, 707953, 712081, 716221, 720373, 724537, 728713, 732901, 737101, 741313, 745537, 749773, 754021, 758281, 762553, 766837, 771133, 775441, 779761, 784093, 788437, 792793, 797161, 801541, 805933, 810337, 814753, 819181, 823621, 828073, 832537, 837013, 841501, 846001, 850513, 855037, 859573, 864121, 868681, 873253, 877837, 882433, 887041, 891661, 896293, 900937, 905593, 910261, 914941, 919633, 924337, 929053, 933781, 938521, 943273, 948037, 952813, 957601, 962401, 967213, 972037, 976873, 981721, 986581, 991453, 996337, 1001233, 1006141, 1011061, 1015993, 1020937, 1025893, 1030861, 1035841, 1040833, 1045837, 1050853, 1055881, 1060921, 1065973, 1071037, 1076113, 1081201, 1086301, 1091413, 1096537, 1101673, 1106821, 1111981, 1117153, 1122337, 1127533, 1132741, 1137961, 1143193, 1148437, 1153693, 1158961, 1164241, 1169533, 1174837, 1180153, 1185481, 1190821, 1196173, 1201537, 1206913, 1212301, 1217701, 1223113, 1228537, 1233973, 1239421, 1244881, 1250353, 1255837, 1261333, 1266841, 1272361, 1277893, 1283437, 1288993, 1294561, 1300141, 1305733, 1311337, 1316953, 1322581, 1328221, 1333873, 1339537, 1345213, 1350901, 1356601, 1362313, 1368037, 1373773, 1379521, 1385281, 1391053, 1396837, 1402633, 1408441, 1414261, 1420093, 1425937, 1431793, 1437661, 1443541, 1449433, 1455337, 1461253, 1467181, 1473121, 1479073, 1485037, 1491013, 1497001, 1503001, 1509013, 1515037, 1521073, 1527121, 1533181, 1539253, 1545337, 1551433, 1557541, 1563661, 1569793, 1575937, 1582093, 1588261, 1594441, 1600633, 1606837, 1613053, 1619281, 1625521, 1631773, 1638037, 1644313, 1650601, 1656901, 1663213, 1669537, 1675873, 1682221, 1688581, 1694953, 1701337, 1707733, 1714141, 1720561, 1726993, 1733437, 1739893, 1746361, 1752841, 1759333, 1765837, 1772353, 1778881, 1785421, 1791973, 1798537, 1805113, 1811701, 1818301, 1824913, 1831537, 1838173, 1844821, 1851481, 1858153, 1864837, 1871533, 1878241, 1884961, 1891693, 1898437, 1905193, 1911961, 1918741, 1925533, 1932337, 1939153, 1945981, 1952821, 1959673, 1966537, 1973413, 1980301, 1987201, 1994113, 2001037, 2007973, 2014921, 2021881, 2028853, 2035837, 2042833, 2049841, 2056861, 2063893, 2070937, 2077993, 2085061, 2092141, 2099233, 2106337, 2113453, 2120581, 2127721, 2134873, 2142037, 2149213, 2156401.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 12909944 values, from 1 to 999999847039153).

n\r 0  1 
2012909944 2 
30129099440 3 
401290994400 4 
505163977258198951639780 5 
60129099440000 6 
70368855536885561844278003688555 7 
806454972000645497200 8 
9086066290043033150000 9 
100516397705163978000258198900 10 
1123472622347263234726302347263117363102347262000

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.