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centered heptagonal n.  and  congruent n.

First numbers that belong to both sets:

22, 71, 148, 197, 253, 316, 386, 463, 638, 736, 1198, 1471, 1933, 2101, 2647, 3046, 3256, 3928, 4166, 4411, 4663, 5461, 5741, 6623, 7246, 8576, 8926, 9647, 10396, 10781, 11173, 11572, 11978, 12391, 13238, 15478, 16423, 17396, 17893, 18397, 18908, 19951, 21022, 23248, 23822, 24991, 26797, 27413, 29303, 30598, 31256, 33272, 33958, 35351, 37493, 38221, 40447, 41966, 42736, 45088, 45886, 47503, 49148, 49981, 50821, 51668, 53383, 55126, 56897, 59606, 61447, 63316, 64261, 65213, 66172, 68111, 70078, 74096, 75118, 77183, 80333, 81397, 84631, 86822, 87928, 90161, 91288, 92422, 94711, 98197, 99373, 102943, 105358, 106576, 111518, 114031, 116572, 117853, 119141, 120436, 123047, 125686, 132406, 135143, 137908, 139301, 140701, 142108, 144943, 147806, 149248, 150697, 153616, 155086, 158047, 162541, 164053, 168631, 171718, 173272, 177976, 179558, 182743, 187573, 189197, 194111, 195763, 197422, 204128, 205822, 209231, 212668, 214397, 216133, 217876, 221383, 224918, 233878, 237511, 241172, 243013, 244861, 246716, 250447, 254206, 256096, 263726, 267583, 273421, 275381, 277348, 281303, 285286, 287288, 293336, 295366, 299447, 305621, 307693, 309772, 313951, 318158, 326656, 328798, 333103, 337436, 339613, 341797, 343988, 348391, 352822, 357281, 364022, 368551, 373108, 375397, 377693, 379996, 384623, 386947, 389278, 391616, 396313, 398672, 401038, 403411, 405791, 412973, 415381, 422647, 427526, 429976, 437368, 439846, 444823, 452341, 454861, 462463, 467566, 470128, 477856, 480446, 485647, 490876, 493501, 496133, 498772, 504071, 509398, 522838, 528263, 533716, 536453, 539197, 541948, 547471, 553022, 564208, 567022, 572671, 578348, 581197, 584053, 592663, 598438, 601336, 610072, 612998, 615931, 618871, 624772, 627733, 630701, 639647, 645646, 648656, 657728, 660766, 666863, 672988, 676061, 679141, 682228, 688423, 694646, 710326, 716647, 722996, 726181, 729373, 732572, 738991, 745438, 761678, 768223, 774796, 778093, 781397, 788026, 791351, 798022, 801368, 811448, 814822, 821591, 831797, 835213, 845503, 848947, 852398, 866272, 869758, 876751, 883772, 887293, 890821, 894356, 901447, 908566, 912136.

Some larger examples :