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decagonal n.  and  evil n.

First numbers that belong to both sets:

10, 27, 85, 126, 175, 232, 297, 540, 742, 1105, 1242, 1701, 2626, 2835, 3052, 3510, 3751, 4000, 4257, 4522, 4795, 5365, 6280, 6930, 8326, 9072, 9850, 10660, 11935, 12825, 13282, 14220, 16705, 17226, 17755, 18292, 19390, 20520, 22876, 24102, 26650, 29326, 31417, 32130, 33580, 34317, 35062, 35815, 38122, 38907, 41310, 42127, 42952, 44626, 45475, 46332, 48070, 48951, 49840, 55342, 57240, 59170, 61132, 62125, 63126, 64135, 65152, 66177, 67210, 68251, 69300, 70357, 72495, 74665, 75762, 81367, 83665, 85995, 87172, 88357, 93177, 95635, 96876, 98125, 100647, 101920, 109726, 112392, 116451, 119197, 121975, 126202, 127627, 129060, 130501, 131950, 133407, 134872, 139315, 140812, 146880, 149962, 151515, 153076, 154645, 157807, 161001, 162610, 164227, 165852, 167485, 169126, 170775, 172432, 174097, 175770, 177451, 179140, 180837, 182542, 184255, 185976, 189442, 192940, 194701, 196470, 203626, 205435, 207252, 212751, 223965, 229680, 231601, 233530, 235467, 241326, 245272, 249250, 251251, 263425, 265482, 267547, 269620, 271701, 277992, 286492, 288637, 290790, 292951, 301675, 303876, 306085, 310527, 321772, 326326, 330912, 333217, 335530, 337851, 340180, 342517, 347215, 349576, 356707, 359100, 361501, 373626, 380997, 390937, 393442, 403542, 424126, 429352, 437251, 442557, 445222, 447895, 450576, 453265, 464101, 466830, 469567, 475065, 477826, 483372, 488950, 491751, 494560, 503035, 517320, 531805, 540592, 543537, 546490, 549451, 552420, 558382, 561375, 564376, 567385, 573427, 576460, 579501, 582550, 585607, 594826, 597915, 601012, 604117, 607230, 626076, 632422, 635607, 645210, 648427, 654885, 667897, 671170, 684342, 687655, 704340, 711070, 717832, 728035, 731452, 734877, 741751, 745200, 752122, 762565, 769567, 773080, 776601, 780130, 787212, 797895, 801472, 808650, 823102, 830376, 834025, 837682, 841347, 852390, 856087, 867226, 870955, 878437, 885951, 893497, 897282, 904876, 931707, 939445, 943326, 951112, 958930, 962851, 966780, 982576, 990522, 994507, 1006510, 1014552, 1018585, 1030732, 1034797, 1038870, 1042951, 1047040, 1051137, 1055242, 1059355, 1063476, 1067605, 1080040, 1084201, 1088370, 1092547, 1109335.

Some larger examples :