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arithmetic n.  and  heptagonal n.

First numbers that belong to both sets:

1, 7, 55, 189, 235, 286, 342, 403, 469, 540, 616, 697, 783, 874, 1071, 1177, 1288, 1651, 1918, 2059, 2205, 2673, 2839, 3010, 3186, 3367, 3553, 3940, 4141, 4347, 4558, 4774, 4995, 5221, 5452, 5688, 6426, 6943, 7209, 8037, 8323, 8614, 9211, 9517, 10465, 10791, 11122, 11799, 12145, 12852, 13213, 13579, 14326, 14707, 15093, 16687, 17098, 17514, 17935, 18361, 19228, 19669, 20115, 20566, 21022, 21483, 21949, 22420, 22896, 23377, 23863, 24354, 24850, 25351, 25857, 26884, 27405, 27931, 28462, 28998, 29539, 30085, 31192, 31753, 32890, 34047, 34633, 35224, 37027, 37638, 38254, 38875, 39501, 40768, 41409, 42055, 42706, 43362, 44023, 44689, 46036, 46717, 47403, 48094, 48790, 50197, 50908, 51624, 52345, 53071, 54538, 55279, 56025, 56776, 58293, 59059, 59830, 60606, 61387, 62173, 62964, 64561, 65367, 66178, 66994, 67815, 68641, 69472, 71149, 71995, 72846, 73702, 74563, 78057, 78943, 79834, 80730, 81631, 82537, 84364, 85285, 86211, 87142, 88078, 89965, 90916, 91872, 92833, 93799, 96727, 97713, 98704, 100701, 101707, 102718, 103734, 104755, 105781, 106812, 108889, 109935, 110986, 112042, 113103, 114169, 115240, 116316, 117397, 118483, 119574, 120670, 121771, 126225, 127351, 128482, 129618, 130759, 131905, 134212, 135373, 136539, 137710, 138886, 140067, 141253, 142444, 143640, 144841, 146047, 149695, 150921, 152152, 155875, 157126, 158382, 159643, 160909, 162180, 164737, 166023, 167314, 169911, 171217, 175165, 176491, 177822, 179158, 180499, 181845, 184552, 185913, 187279, 188650, 190026, 191407, 192793, 194184, 195580, 196981, 198387, 199798, 201214, 202635, 204061, 205492, 206928, 209815, 212722, 214183, 215649, 217120, 220077, 221563, 223054, 226051, 227557, 232105, 233631, 235162, 236698, 238239, 239785, 241336, 242892, 244453, 246019, 247590, 249166, 250747, 252333, 253924, 257121, 258727, 260338, 261954, 265201, 266832, 268468, 270109, 273406, 275062, 276723, 278389, 280060, 281736, 285103, 286794, 290191, 291897, 293608, 295324, 297045, 298771, 300502, 302238, 303979, 310993, 312759, 314530, 318087.

Some larger examples :