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heptagonal n.  and  self n.

First numbers that belong to both sets:

1, 7, 1177, 7756, 10144, 13213, 19669, 25857, 31753, 34633, 44689, 62173, 65367, 69472, 73702, 78057, 110986, 115240, 122877, 149695, 163456, 180499, 201214, 209815, 214183, 217120, 221563, 239785, 302238, 303979, 318087, 338008, 343546, 383572, 403407, 434097, 450925, 494395, 496621, 553896, 592192, 609349, 664866, 680427, 693532, 706762, 720117, 739024, 749938, 814246, 817102, 822829, 828576, 848848, 857611, 872316, 890127, 978751, 1029447, 1058526, 1065043, 1078137, 1081423, 1134679, 1209996, 1230957, 1248562, 1255639, 1266292, 1284147, 1298521, 1302127, 1427706, 1450467, 1484946, 1504276, 1508157, 1539385, 1618855, 1663416, 1721005, 1750167, 1792252, 1804975, 1860628, 1917126, 1956735, 1983366, 2059798, 2073436, 2188836, 2259576, 2326615, 2429011, 2438878, 2478546, 2548735, 2553786, 2635282, 2650705, 2671339, 2786256, 2871352, 2919781, 2936014, 3084136, 3100819, 3139921, 3145527, 3168001, 3196206, 3224536, 3230217, 3275845, 3391315, 3408808, 3414649, 3455676, 3491037, 3538465, 3544416, 3580227, 3640312, 3658435, 3737488, 3817386, 3866974, 3910626, 3973411, 4171222, 4184149, 4197096, 4236057, 4294836, 4334247, 4387075, 4440223, 4460236, 4588030, 4656015, 4690195, 4697046, 4807342, 4828165, 4890904, 4897900, 4968135, 5053077, 5102959, 5124412, 5160267, 5239588, 5261326, 5414752, 5444226, 5555466, 5600277, 5660305, 5811775, 5819401, 5834668, 5849955, 6003925, 6136372, 6191329, 6365646, 6429634, 6566671, 6591004, 6623518, 6696967, 6820282, 6853356, 6869923, 6911428, 6936391, 7095535, 7273531, 7290598, 7359066, 7410627, 7557694, 7758967, 7829595, 7953964, 7962885, 8016516, 8025472, 8070327, 8169448, 8369505, 8406139, 8424486, 8516521, 8599780, 8664817, 8880235, 8927415, 8974720, 8993677, 9041157, 9069705, 9117385, 9126936, 9280432, 9309355, 9396394, 9435208, 9709146, 9837664, 10107286, 10137469, 10157616, 10218177, 10360186, 10370367, 10451995, 10657465, 10667791, 10688458, 10771326, 10864935, 10917115, 10927566, 11000863, 11095462, 11201047, 11488624, 11520802, 11542279, 11563776, 11574532, 11747308, 11986965, 12008872, 12030799, 12129718, 12217986, 12373225, 12607921, 12641629, 12890196, 13072492, 13106815, 13152649, 13498954, 13533832, 13580406, 13592062, 13697191, 13779238, 14050546, 14062402, 14086129, 14109876, 14169331, 14181237, 14228911, 14360427, 14456455, 14734318, 14758605, 14831586, 15014826, 15100723, 15211522, 15248545, 15359884, 15409498, 15496515, 15571296, 15683805, 15973168, 16011106, 16303459, 16392961, 16418578, 16662937, 16701685, 16961155.

Some larger examples :