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centered heptagonal n.  and  Duffinian n.

First numbers that belong to both sets:

8, 253, 841, 1331, 2101, 3473, 4411, 5461, 6623, 6931, 7897, 9647, 12811, 14113, 15947, 16423, 17893, 19951, 22121, 22681, 24403, 24991, 26797, 27413, 31921, 32593, 35351, 38221, 40447, 43513, 44297, 47503, 49981, 53383, 61447, 64261, 73081, 77183, 81397, 85723, 90161, 94711, 98197, 99373, 102943, 107801, 109033, 117853, 119141, 123047, 128353, 129697, 133771, 135143, 140701, 144943, 146371, 152153, 162541, 164053, 170171, 174833, 181147, 182743, 189197, 194111, 195763, 200761, 214397, 221383, 223147, 228481, 235691, 243013, 250447, 265651, 267583, 273421, 275381, 281303, 283291, 313951, 322393, 324521, 330947, 341797, 348391, 350603, 359521, 366283, 375397, 377693, 386947, 396313, 403411, 405791, 412973, 422647, 434897, 442331, 444823, 452341, 454861, 462463, 483043, 493501, 496133, 504071, 512072, 514753, 517441, 525547, 539197, 550243, 558601, 561401, 604241, 615931, 618871, 642643, 651673, 663811, 666863, 679141, 704033, 713483, 716647, 738991, 755161, 768223, 778093, 791351, 794683, 804721, 818203, 821591, 831797, 845503, 848947, 862793, 887293, 915713, 919297, 930091, 948221, 962851, 988723, 992447, 1003661, 1007413, 1033873, 1049147, 1052983, 1068397, 1080031, 1095641, 1099561, 1111363, 1115311, 1131173, 1147147, 1179431, 1191653, 1208047, 1212163, 1224553, 1228697, 1241171, 1245343, 1257901, 1274743, 1278971, 1291697, 1308763, 1313047, 1343231, 1347571, 1360633, 1365001, 1413511, 1417963, 1435841, 1449323, 1471933, 1485583, 1490147, 1526911, 1564123, 1582897, 1597051, 1616021, 1620781, 1635103, 1654297, 1659113, 1673603, 1678447, 1697893, 1737121, 1771813, 1776797, 1811881, 1816921, 1832083, 1852397, 1857493, 1872823, 1877947, 1914011, 1919191, 1939981, 1955647, 1960883, 1981897, 2003023, 2018941, 2061697, 2088647, 2110333, 2126671, 2132131, 2170547, 2176063, 2198197, 2214871, 2220443, 2237201, 2242801, 2282197, 2287853, 2304863, 2350531, 2356271, 2379301, 2396647, 2402443, 2449063, 2490223, 2496131, 2513897, 2519833, 2537683, 2561581, 2567573, 2585591, 2591611, 2609713, 2658293, 2713481, 2732003, 2763013, 2806721, 2863421, 2888803, 2907913, 2914297, 2933491, 2939903, 2959181, 2965621, 2984983, 3010897, 3017393, 3036923, 3043447, 3063061, 3069613, 3095891, 3142147, 3148783, 3168733, 3175397, 3195431, 3222241, 3255911, 3276197, 3282973, 3330601, 3337433, 3357971.

Some larger examples :