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centered decagonal numbers
Figurate numbers of the form 5n(n-1) + 1. more

The first 600 centered decagonal numbers :
1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, 1201, 1361, 1531, 1711, 1901, 2101, 2311, 2531, 2761, 3001, 3251, 3511, 3781, 4061, 4351, 4651, 4961, 5281, 5611, 5951, 6301, 6661, 7031, 7411, 7801, 8201, 8611, 9031, 9461, 9901, 10351, 10811, 11281, 11761, 12251, 12751, 13261, 13781, 14311, 14851, 15401, 15961, 16531, 17111, 17701, 18301, 18911, 19531, 20161, 20801, 21451, 22111, 22781, 23461, 24151, 24851, 25561, 26281, 27011, 27751, 28501, 29261, 30031, 30811, 31601, 32401, 33211, 34031, 34861, 35701, 36551, 37411, 38281, 39161, 40051, 40951, 41861, 42781, 43711, 44651, 45601, 46561, 47531, 48511, 49501, 50501, 51511, 52531, 53561, 54601, 55651, 56711, 57781, 58861, 59951, 61051, 62161, 63281, 64411, 65551, 66701, 67861, 69031, 70211, 71401, 72601, 73811, 75031, 76261, 77501, 78751, 80011, 81281, 82561, 83851, 85151, 86461, 87781, 89111, 90451, 91801, 93161, 94531, 95911, 97301, 98701, 100111, 101531, 102961, 104401, 105851, 107311, 108781, 110261, 111751, 113251, 114761, 116281, 117811, 119351, 120901, 122461, 124031, 125611, 127201, 128801, 130411, 132031, 133661, 135301, 136951, 138611, 140281, 141961, 143651, 145351, 147061, 148781, 150511, 152251, 154001, 155761, 157531, 159311, 161101, 162901, 164711, 166531, 168361, 170201, 172051, 173911, 175781, 177661, 179551, 181451, 183361, 185281, 187211, 189151, 191101, 193061, 195031, 197011, 199001, 201001, 203011, 205031, 207061, 209101, 211151, 213211, 215281, 217361, 219451, 221551, 223661, 225781, 227911, 230051, 232201, 234361, 236531, 238711, 240901, 243101, 245311, 247531, 249761, 252001, 254251, 256511, 258781, 261061, 263351, 265651, 267961, 270281, 272611, 274951, 277301, 279661, 282031, 284411, 286801, 289201, 291611, 294031, 296461, 298901, 301351, 303811, 306281, 308761, 311251, 313751, 316261, 318781, 321311, 323851, 326401, 328961, 331531, 334111, 336701, 339301, 341911, 344531, 347161, 349801, 352451, 355111, 357781, 360461, 363151, 365851, 368561, 371281, 374011, 376751, 379501, 382261, 385031, 387811, 390601, 393401, 396211, 399031, 401861, 404701, 407551, 410411, 413281, 416161, 419051, 421951, 424861, 427781, 430711, 433651, 436601, 439561, 442531, 445511, 448501, 451501, 454511, 457531, 460561, 463601, 466651, 469711, 472781, 475861, 478951, 482051, 485161, 488281, 491411, 494551, 497701, 500861, 504031, 507211, 510401, 513601, 516811, 520031, 523261, 526501, 529751, 533011, 536281, 539561, 542851, 546151, 549461, 552781, 556111, 559451, 562801, 566161, 569531, 572911, 576301, 579701, 583111, 586531, 589961, 593401, 596851, 600311, 603781, 607261, 610751, 614251, 617761, 621281, 624811, 628351, 631901, 635461, 639031, 642611, 646201, 649801, 653411, 657031, 660661, 664301, 667951, 671611, 675281, 678961, 682651, 686351, 690061, 693781, 697511, 701251, 705001, 708761, 712531, 716311, 720101, 723901, 727711, 731531, 735361, 739201, 743051, 746911, 750781, 754661, 758551, 762451, 766361, 770281, 774211, 778151, 782101, 786061, 790031, 794011, 798001, 802001, 806011, 810031, 814061, 818101, 822151, 826211, 830281, 834361, 838451, 842551, 846661, 850781, 854911, 859051, 863201, 867361, 871531, 875711, 879901, 884101, 888311, 892531, 896761, 901001, 905251, 909511, 913781, 918061, 922351, 926651, 930961, 935281, 939611, 943951, 948301, 952661, 957031, 961411, 965801, 970201, 974611, 979031, 983461, 987901, 992351, 996811, 1001281, 1005761, 1010251, 1014751, 1019261, 1023781, 1028311, 1032851, 1037401, 1041961, 1046531, 1051111, 1055701, 1060301, 1064911, 1069531, 1074161, 1078801, 1083451, 1088111, 1092781, 1097461, 1102151, 1106851, 1111561, 1116281, 1121011, 1125751, 1130501, 1135261, 1140031, 1144811, 1149601, 1154401, 1159211, 1164031, 1168861, 1173701, 1178551, 1183411, 1188281, 1193161, 1198051, 1202951, 1207861, 1212781, 1217711, 1222651, 1227601, 1232561, 1237531, 1242511, 1247501, 1252501, 1257511, 1262531, 1267561, 1272601, 1277651, 1282711, 1287781, 1292861, 1297951, 1303051, 1308161, 1313281, 1318411, 1323551, 1328701, 1333861, 1339031, 1344211, 1349401, 1354601, 1359811, 1365031, 1370261, 1375501, 1380751, 1386011, 1391281, 1396561, 1401851, 1407151, 1412461, 1417781, 1423111, 1428451, 1433801, 1439161, 1444531, 1449911, 1455301, 1460701, 1466111, 1471531, 1476961, 1482401, 1487851, 1493311, 1498781, 1504261, 1509751, 1515251, 1520761, 1526281, 1531811, 1537351, 1542901, 1548461, 1554031, 1559611, 1565201, 1570801, 1576411, 1582031, 1587661, 1593301, 1598951, 1604611, 1610281, 1615961, 1621651, 1627351, 1633061, 1638781, 1644511, 1650251, 1656001, 1661761, 1667531, 1673311, 1679101, 1684901, 1690711, 1696531, 1702361, 1708201, 1714051, 1719911, 1725781, 1731661, 1737551, 1743451, 1749361, 1755281, 1761211, 1767151, 1773101, 1779061, 1785031, 1791011, 1797001.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 14142136 values, from 1 to 999999982501801).

n\r 0  1 
2014142136 2 
3094280914714045 3 
40707106807071068 4 
5014142136000 5 
6094280910004714045 6 
70404061104040610404061020203050 7 
803535534035355340353553403535534 8 
9031426974714045031426970031426970 9 
1001414213600000000 10 
1125712972571297257129800025712980128564925712970

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.