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heptagonal n.  and  lucky n.

First numbers that belong to both sets:

1, 7, 189, 235, 2059, 6175, 8037, 9211, 17935, 23377, 38875, 42055, 44023, 46717, 62173, 64561, 65367, 93799, 101707, 104755, 114169, 121771, 126225, 130759, 146047, 164737, 187279, 192793, 221563, 244453, 246019, 258727, 263575, 265201, 271755, 278389, 325261, 327067, 334341, 369985, 371911, 387499, 393427, 417589, 444577, 459459, 468073, 476767, 496621, 521437, 523723, 530611, 542191, 577681, 580087, 616777, 629257, 636805, 639331, 659719, 698809, 733597, 741745, 788767, 808549, 834343, 857611, 878233, 938503, 941569, 953883, 988159, 1013467, 1255639, 1273419, 1302127, 1312975, 1345789, 1375297, 1386445, 1405125, 1420159, 1512043, 1523731, 1527637, 1543311, 1586827, 1618855, 1704451, 1721005, 1834837, 1856317, 1873591, 1890945, 1908379, 1943487, 1974469, 2179489, 2193517, 2212291, 2250079, 2312167, 2326615, 2424085, 2443819, 2508507, 2589283, 2796823, 2833965, 2925187, 2946861, 3006877, 3034357, 3168001, 3258697, 3304525, 3414649, 3485131, 3532519, 3538465, 3700897, 3755851, 3774259, 3929409, 3979717, 4049413, 4074907, 4151869, 4262131, 4334247, 4717629, 4911907, 5045971, 5081551, 5167453, 5196247, 5246829, 5275843, 5570383, 5607763, 5750947, 5788927, 5842309, 5872923, 5880589, 6003925, 6120715, 6152049, 6183463, 6254437, 6286111, 6373627, 6405601, 6664273, 6696967, 6737947, 6861637, 6994813, 7036693, 7230951, 7376233, 7402021, 7445101, 7583797, 7653625, 7679893, 7714987, 7758967, 7785415, 7971811, 7998619, 8007565, 8115307, 8360359, 8618337, 8739445, 8776879, 8851987, 9261175, 9425497, 9659941, 9967027.