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congruent n.  and  heptagonal n.

First numbers that belong to both sets:

7, 34, 55, 112, 148, 189, 286, 342, 469, 540, 616, 783, 1071, 1404, 1525, 1651, 1782, 1918, 2059, 2205, 2356, 2512, 2839, 3367, 3940, 4141, 4558, 4774, 5221, 5688, 6175, 6943, 7480, 7756, 8037, 8614, 8910, 9517, 10791, 11458, 11799, 12496, 12852, 13213, 13950, 14326, 15093, 15484, 16687, 17935, 19228, 19669, 20566, 21022, 21949, 22420, 22896, 23863, 24354, 25351, 26368, 27405, 28462, 28998, 30085, 31192, 32319, 34047, 35224, 35820, 36421, 37638, 38254, 39501, 40132, 40768, 42055, 44023, 46036, 46717, 48094, 48790, 50197, 50908, 51624, 52345, 53071, 55279, 57532, 58293, 59830, 60606, 62173, 62964, 63760, 65367, 66178, 67815, 69472, 71149, 72846, 73702, 75429, 77176, 78943, 79834, 80730, 81631, 83448, 85285, 86211, 87142, 88078, 89965, 91872, 93799, 96727, 99700, 100701, 102718, 103734, 105781, 106812, 109935, 112042, 113103, 116316, 117397, 119574, 120670, 122877, 123988, 125104, 126225, 127351, 130759, 133056, 134212, 135373, 137710, 138886, 141253, 143640, 146047, 149695, 152152, 154629, 157126, 158382, 160909, 166023, 169911, 172528, 173844, 175165, 177822, 179158, 181845, 183196, 184552, 187279, 188650, 191407, 194184, 195580, 196981, 199798, 201214, 204061, 205492, 206928, 208369, 209815, 211266, 212722, 214183, 220077, 223054, 224550, 226051, 227557, 230584, 233631, 238239, 241336, 244453, 247590, 249166, 252333, 253924, 258727, 263575, 266832, 268468, 270109, 271755, 273406, 275062, 278389, 280060, 285103, 290191, 295324, 297045, 300502, 302238, 305725, 307476, 309232, 312759, 318087, 325261, 328878, 330694, 332515, 334341, 338008, 341695, 347263, 351000, 354757, 358534, 360430, 364237, 368064, 371911, 377719, 383572, 385533, 389470, 391446, 395413, 397404, 403407, 409455, 411481, 415548, 417589, 421686, 423742, 427869, 429940, 436183, 440370, 442471, 446688, 448804, 450925, 455182, 457318, 459459, 461605, 465912, 470239, 476767, 481144, 485541, 489958, 492174, 494395, 496621, 501088, 505575, 507826, 512343, 519156, 521437, 526014, 528310, 532917, 535228, 537544, 542191, 549199, 556252, 558613, 563350, 565726, 570493, 572884.

Some larger examples :