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centered heptagonal n.  and  gapful n.

First numbers that belong to both sets:

253, 1331, 24403, 106576, 119141, 133771, 140701, 153616, 269522, 811448, 1179431, 1220416, 1365001, 1369376, 1413511, 1435841, 1499296, 1616021, 1639891, 1663936, 1693021, 1914011, 1971376, 2220443, 2367772, 2449063, 2695022, 2725822, 2763013, 2907913, 3447697, 4018393, 4154536, 5325328, 7012741, 7102201, 7827821, 8446768, 8898506, 10240336, 10408651, 10541861, 10602691, 10663696, 11020976, 11083171, 11145541, 11283371, 11460016, 11843161, 12245696, 12641651, 12708256, 13098016, 13233781, 13383931, 13452461, 13576256, 13993001, 14063071, 14217841, 14430256, 14845391, 14932016, 15354256, 15737821, 15871696, 16397711, 16564801, 16641031, 16794016, 17241631, 17319401, 17334976, 17491111, 17789696, 18186421, 18346336, 19172791, 19336976, 19900441, 19917136, 20455072, 20539772, 20556733, 21483022, 23342572, 24328963, 24347422, 24439822, 25072783, 25467772, 26056493, 26497633, 26826073, 27273653, 27489022, 28299223, 28578572, 28678672, 29101003, 29791322, 31974272, 32080147, 32719072, 36120547, 39103072, 39926272, 40210486, 41333363, 41501923, 43132636, 44121176, 45574453, 46004876, 46667083, 47025616, 47772656, 48812716, 51649928, 52243213, 53275958, 53686403, 55622638, 57309568, 58076908, 59655793, 59800378, 66915647, 72124711, 74689231, 80589608, 83401648, 84223756, 86053528, 88711666, 89984896, 90945772, 92378672, 100534841, 101701216, 102836371, 103026176, 104130496, 104512661, 104933851, 105125581, 105471136, 106627081, 106820351, 107246161, 107828176, 108957871, 109192336, 110329136, 111353341, 111708976, 113097391, 113535521, 113734951, 114134336, 115296511, 115497481, 115537696, 115940231, 116706976, 117719701, 118126016, 120209111, 120619696, 122020921, 122062256, 122475991, 122683121, 123264016, 124304741, 124513411, 124722256, 124973101, 126820331, 127284256, 128766016, 129403681, 130000256, 131283251, 131497696, 131755261, 131970091, 133651771, 133868141, 134128016, 134344771, 135648976, 136259761, 136915696, 138452336, 138937051, 140884381, 141150976, 141373331, 141595861, 142711136, 143337601, 143561671, 144010336, 144055241, 145586176, 146037991, 148353136, 148809221, 149952496, 150824311, 151284176, 151330201, 151560431, 152899216, 153362231, 153594001, 154104511, 155734496, 156155021, 157373056, 158737216, 159020191, 160391456, 161103041, 161625871, 161863801, 163295056, 163725661, 163965131, 164492581, 164972816, 166369456, 166610851, 168062896, 169569961, 171034816, 171720571, 172260341, 172505971, 172751776, 174180896, 174427891, 174675061, 175219451, 175913536, 177405481, 178953776, 180458531, 180709936, 182171536, 182676901, 183233611, 183486941, 183943376, 185468921, 185723791, 186285121, 187051936, 188538911, 188847296, 190341376, 191685901, 192152416, 193972031, 194545681, 194806711, 195329296, 196848751, 197111321, 197163856, 197689591, 198690416, 204427322, 207326393, 207380272, 207649772, 209487013, 210625822.

Some larger examples :