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decagonal n.  and  pernicious n.

First numbers that belong to both sets:

10, 52, 370, 451, 637, 855, 976, 1387, 1540, 1870, 2047, 2232, 2425, 3277, 5076, 5662, 6601, 7267, 9457, 10251, 11077, 12376, 16192, 18837, 19951, 21097, 21682, 22275, 23485, 24727, 25360, 26001, 27972, 28645, 30015, 30712, 32851, 36576, 37345, 39700, 43785, 50737, 53476, 54405, 56287, 60147, 71422, 76867, 77980, 79101, 82512, 89550, 90751, 94402, 99382, 103201, 104490, 105787, 107092, 108405, 111055, 115090, 124785, 136345, 137826, 142317, 145351, 148417, 187705, 191187, 200032, 201825, 210910, 214600, 222076, 227767, 237412, 243295, 247257, 253260, 255277, 257302, 259335, 273790, 275887, 280105, 295120, 297297, 315001, 319507, 324045, 351945, 354322, 366327, 368752, 371185, 376075, 383470, 385951, 388440, 398476, 401005, 408640, 411201, 413770, 416347, 421525, 426735, 431977, 439900, 455962, 461380, 472312, 480595, 486157, 497377, 500202, 508725, 511582, 514447, 523090, 525987, 534726, 570402, 591745, 619762, 622915, 629245, 638800, 642001, 661375, 664632, 677740, 690976, 694305, 700987, 707701, 714447, 721225, 738310, 748657, 755595, 766062, 783667, 794326, 805057, 812251, 815860, 819477, 826735, 845020, 848701, 882190, 889720, 908685, 912502, 920160, 947215, 974662, 986545, 998500, 1022626, 1026675, 1071742, 1075887, 1100925, 1105126, 1113552, 1122010, 1151865, 1156162, 1164780, 1173430, 1203957, 1217160, 1234876, 1239325, 1243782, 1248247, 1275205, 1293337, 1307020, 1325376, 1339227, 1367145, 1395351, 1414315, 1423845, 1428622, 1438200, 1457452, 1486570, 1491451, 1501237, 1530787, 1540701, 1550647, 1600857, 1610995, 1641601, 1646730, 1651867, 1667326, 1672495, 1688050, 1693251, 1703677, 1714135, 1729882, 1777555, 1782892, 1788237, 1793590, 1798951, 1804320, 1809697, 1815082, 1842127, 1847560, 1858450, 1863907, 1874845, 1885815, 1891312, 1907851, 1941145, 1946722, 1974727, 1980352, 1985985, 2008597, 2025640, 2037042, 2054205, 2077201, 2100325, 2106126, 2117752, 2152822, 2164576, 2182267, 2200030, 2217865, 2229795, 2235772, 2241757, 2314201, 2320290, 2332492, 2338605, 2344726, 2350855, 2363137, 2425027, 2443750, 2450007, 2456272, 2468826, 2475115, 2487717, 2506680, 2513017, 2532076, 2570410, 2576827, 2589685, 2596126, 2621970, 2680587, 2700270, 2706847, 2713432, 2726626, 2739852, 2773057, 2799765, 2806462, 2833330, 2846812, 2853565.

Some larger examples :