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centered heptagonal n.  and  evil n.

First numbers that belong to both sets:

43, 71, 106, 197, 547, 736, 1198, 1331, 2458, 3046, 3256, 3473, 4166, 5188, 5741, 6322, 6623, 7568, 8233, 8926, 10018, 10396, 11173, 11978, 12811, 16906, 17396, 17893, 18397, 18908, 19426, 20483, 21568, 22121, 23822, 24403, 26797, 27413, 28666, 29303, 32593, 33958, 36058, 36772, 37493, 38221, 38956, 41203, 41966, 42736, 43513, 45088, 45886, 47503, 48322, 51668, 52522, 55126, 56008, 56897, 60523, 62378, 63316, 71072, 73081, 74096, 77183, 80333, 81397, 83546, 86822, 87928, 89041, 90161, 93563, 94711, 97028, 98197, 104147, 105358, 107801, 109033, 110272, 112771, 116572, 117853, 120436, 121738, 125686, 128353, 129697, 137908, 142108, 143522, 144943, 146371, 147806, 150697, 152153, 159538, 161036, 162541, 168631, 170171, 171718, 173272, 174833, 177976, 181147, 190828, 192466, 195763, 197422, 204128, 205822, 209231, 210946, 212668, 216133, 217876, 223147, 235691, 243013, 248578, 254206, 256096, 261808, 267583, 269522, 275381, 281303, 291313, 293336, 297403, 299447, 301498, 305621, 309772, 328798, 330947, 333103, 337436, 341797, 343988, 348391, 350603, 355048, 357281, 359521, 364022, 370826, 373108, 379996, 382306, 384623, 391616, 393961, 401038, 405791, 408178, 412973, 415381, 429976, 437368, 439846, 449828, 457388, 465011, 467566, 472697, 477856, 480446, 488258, 490876, 496133, 498772, 504071, 506731, 509398, 512072, 517441, 525547, 539197, 547471, 555808, 558601, 564208, 572671, 575506, 589786, 595547, 598438, 601336, 604241, 618871, 624772, 627733, 633676, 636658, 645646, 648656, 663811, 666863, 676061, 682228, 688423, 691531, 700897, 704033, 710326, 713483, 716647, 738991, 742211, 748672, 758416, 764947, 768223, 774796, 781397, 788026, 791351, 794683, 804721, 808081, 814822, 821591, 824986, 828388, 831797, 835213, 838636, 842066, 845503, 869758, 873251, 880258, 883772, 890821, 894356, 897898, 901447, 908566, 912136, 915713, 930091, 948221, 951868, 955522, 959183, 962851, 966526, 985006, 1003661, 1007413, 1022491, 1026278, 1030072, 1052983, 1056826, 1060676, 1064533, 1068397, 1072268, 1076146, 1091728, 1095641, 1107422, 1111363, 1119266, 1127197, 1131173, 1135156, 1171318, 1179431, 1183498, 1208047, 1224553, 1237006, 1241171.

Some larger examples :