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aban n.  and  heptagonal n.

First numbers that belong to both sets:

1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, 616, 697, 783, 874, 970, 1000773, 11000863, 17000248, 35000797, 39000325, 41000175, 78000111, 108000963, 122000011, 179000917, 183000006, 187000029, 212000389, 242000044, 254000880, 301000363, 402000381, 423000648, 538000245, 609000748, 648000850, 989000415, 1011000085, 1023000759, 1131000345, 1382000092, 1466000316, 1483000306, 1578000754, 1621000044, 1670000521, 1858000717, 1861000714, 2036000803, 2045000101, 2420000253, 3106000888, 3594000766, 3726000181, 3969000295, 4661000334, 4777000353, 4949000883, 5033000599, 5194000531, 5681000745, 5965000252, 6654000816, 7006000203, 7363000845, 7690000417, 8117000431, 8246000412, 8434000098, 8755000443, 8943000535, 9622000744, 9640000377, 9705000631, 10214000524, 10956000700, 11450000926, 11657000635, 11795000328, 12029000841, 12266000221, 13163000767, 13390000785, 13787000217, 13983000178, 14655000394, 14719000806, 15090000622, 15503000638, 15818000524, 15857000947, 16088000670, 16292000232, 16632000715, 16915000456, 17772000019, 18626000166, 19846000363, 19983000955, 21378000613, 22143000753, 22522000690, 23336000640, 24133000126, 24662000227, 25123000921, 25992000115, 26182000417, 26287000597, 26307000031, 26403000408, 26910000625, 27502000735, 28421000388, 28469000853, 29557000123, 29918000970, 30339000367, 31134000646, 31757000562, 33572000398, 34499000752, 36336000364, 36934000702, 37024000020, 37080000742, 37233000553, 37412000406, 37983000411, 38590000047, 38963000941, 42432000580, 42882000949, 43478000626, 45538000794, 46365000364, 46689000714, 48344000410, 48797000685, 48955000336, 49046000791, 49446000286, 49996000516, 50918000419, 51123000501, 54137000106, 56025000450, 57313000186, 57886000641, 58390000582, 58821000165, 58877000728, 59467000905, 61221000628, 61275000787, 61755000649, 61869000519, 62987000509, 63752000715, 64969000312, 65797000056, 67899000807, 68458000384, 70438000780, 72522000520, 72718000425, 73617000601, 73854000007, 75004000435, 76080000088, 76121000820, 76279000426, 76768000210, 77154000550, 77299000240, 79411000351, 79884000706, 79943000977, 80501000895, 80765000694, 81151000308, 81715000933, 82349000383, 84162000780, 85528000978, 86433000394, 86633000059, 87254000770, 88968000321, 89854000348, 91228000282, 91576000116, 92105000208, 93128000581, 93468000373, 99043000641, 99280000684, 100347000502, 102406000572, 103009000942, 103142000133, 103683000775, 103793000773, 108449000793, 108915000975, 109081000314, 109382000202, 109980000508, 110968000198, 111183000592, 112714000389, 112834000852, 113566000860, 114418000323, 114464000476, 115459000684, 116276000428, 116331000919, 119540000899, 120749000302, 122878000951, 124165000414, 127387000962, 128804000164, 129995000356, 131929000021, 133735000428, 134103000681, 134242000101, 136512000307, 137310000664, 138329000982, 138675000321, 139835000284, 140029000558, 140402000248, 140530000066, 142654000126, 142697000992, 144456000430, 144569000979, 147048000532, 148714000677, 150970000390, 151750000129, 151888000761, 152972000194, 153399000139, 156735000778, 158868000361, 159288000274, 159883000915, 160012000672, 160317000873, 160763000185, 162134000244, 162269000095, 162492000145, 164520000106, 167605000675, 167842000498, 168641000854, 169248000916, 170967000439, 171835000702, 177422000400, 178134000489, 178925000401, 179880000444, 181586000898, 181741000888, 183208000639, 183491000433, 184268000466, 184704000642.

Some larger examples :