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centered pentagonal n.  and  pernicious n.

First numbers that belong to both sets:

6, 31, 76, 181, 276, 331, 391, 601, 681, 856, 1051, 1156, 1756, 1891, 2176, 2326, 2641, 2976, 3151, 3331, 4101, 4306, 4516, 5176, 5406, 5641, 7426, 7701, 10081, 10401, 12426, 13876, 15016, 16606, 18276, 18706, 19141, 20476, 20931, 24256, 25251, 25756, 29431, 29976, 30526, 32206, 32776, 34516, 35106, 36906, 38751, 39376, 40006, 41281, 44556, 45226, 46581, 47266, 49351, 51481, 52926, 53656, 55131, 55876, 66016, 66831, 67651, 70981, 73531, 77881, 82356, 86026, 88831, 91681, 97516, 100501, 102516, 108681, 111831, 115026, 117181, 123766, 124881, 128256, 129391, 130531, 136306, 137476, 142206, 148231, 150676, 151906, 164481, 176226, 178891, 181576, 189751, 191131, 193906, 196701, 202351, 203776, 212431, 218301, 221266, 228766, 239476, 242581, 245706, 247276, 258406, 261631, 264876, 266506, 271426, 276391, 286456, 294981, 296701, 305376, 310641, 314176, 319516, 323101, 333976, 335806, 360051, 375391, 377331, 383181, 389076, 391051, 407031, 409051, 421276, 423331, 427456, 429526, 431601, 450501, 456891, 463326, 469806, 474151, 485101, 493951, 505126, 507376, 511891, 514156, 525556, 541726, 548731, 551076, 565251, 570016, 572406, 584431, 589276, 603931, 611326, 613801, 616281, 628756, 636301, 638826, 643891, 646431, 656641, 677301, 690376, 695641, 698281, 700926, 741201, 743926, 757626, 765906, 768676, 771451, 774231, 793831, 810826, 816531, 833766, 836656, 859956, 862891, 865831, 871726, 874681, 883576, 886551, 892516, 907516, 910531, 916576, 922641, 925681, 947101, 953266, 956356, 959451, 968766, 971881, 978126, 996981, 1000141, 1019206, 1022401, 1032016, 1038451, 1041676, 1044906, 1061131, 1064391, 1074201, 1080766, 1084056, 1093956, 1134006, 1154301, 1161106, 1167931, 1178206, 1233766, 1251391, 1265581, 1297801, 1312251, 1319506, 1323141, 1326781, 1330426, 1334076, 1359766, 1363456, 1367151, 1378266, 1381981, 1389426, 1423176, 1434516, 1438306, 1445901, 1453516, 1461151, 1488031, 1495756, 1503501, 1511266, 1515156, 1519051, 1530766, 1534681, 1542526, 1546456, 1562226, 1590016, 1638226, 1650391, 1662601, 1666681, 1678951, 1683051, 1687156, 1695381, 1707756, 1711891, 1728481, 1745151, 1749331, 1766101, 1774516, 1791406, 1799881, 1804126, 1829701, 1851151, 1855456.

Some larger examples :