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evil n.  and  heptagonal n.

First numbers that belong to both sets:

18, 34, 189, 235, 469, 540, 616, 697, 783, 874, 970, 1071, 1525, 1782, 2059, 2205, 2673, 3010, 3186, 4347, 4774, 4995, 5221, 5452, 5688, 6426, 6682, 7209, 8323, 8614, 9211, 9828, 10144, 10465, 11122, 11458, 11799, 12852, 13950, 15093, 15880, 16281, 17098, 17514, 18792, 19669, 20115, 20566, 21483, 21949, 22420, 23377, 23863, 24354, 27405, 28462, 30085, 30636, 32319, 32890, 34047, 35224, 37027, 37638, 39501, 41409, 42706, 44023, 44689, 45360, 48094, 48790, 50197, 56025, 57532, 58293, 59059, 59830, 61387, 66178, 67815, 70308, 71149, 72846, 75429, 76300, 78057, 78943, 80730, 85285, 87142, 89019, 89965, 91872, 92833, 94770, 96727, 99700, 105781, 106812, 109935, 110986, 112042, 113103, 115240, 120670, 121771, 123988, 125104, 127351, 129618, 133056, 137710, 138886, 142444, 143640, 146047, 148474, 149695, 150921, 155875, 158382, 159643, 162180, 163456, 164737, 167314, 169911, 172528, 173844, 175165, 176491, 179158, 183196, 184552, 185913, 187279, 195580, 196981, 198387, 202635, 204061, 205492, 206928, 211266, 212722, 215649, 218596, 220077, 224550, 229068, 230584, 233631, 235162, 236698, 242892, 244453, 247590, 252333, 255520, 257121, 258727, 260338, 261954, 263575, 270109, 271755, 273406, 276723, 278389, 280060, 281736, 283417, 286794, 288490, 293608, 300502, 302238, 303979, 305725, 314530, 318087, 321664, 323460, 328878, 339849, 347263, 349129, 354757, 366148, 369985, 375778, 377719, 383572, 387499, 389470, 399400, 403407, 407434, 409455, 411481, 417589, 421686, 434097, 438274, 444577, 446688, 455182, 457318, 459459, 465912, 476767, 478953, 481144, 485541, 487747, 494395, 498852, 503329, 505575, 507826, 510082, 512343, 519156, 521437, 528310, 530611, 532917, 537544, 539865, 544522, 551545, 560979, 563350, 565726, 568107, 575280, 584914, 589761, 601966, 604422, 606883, 609349, 619263, 621754, 624250, 626751, 629257, 631768, 641862, 649485, 657153, 662290, 667447, 672624, 683038, 690901, 701455, 704106, 709423, 712089, 717436, 720117, 728190, 730891, 736308, 741745, 747202, 752679, 755425, 758176, 760932, 763693, 766459, 772006, 774787, 780364, 783160, 794394, 797215.

Some larger examples :