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centered heptagonal n.  and  economical n.

First numbers that belong to both sets:

1, 43, 71, 106, 197, 463, 547, 841, 953, 1072, 1198, 1331, 1471, 1618, 1933, 2647, 2843, 3697, 4663, 5741, 8233, 8576, 9283, 10018, 10781, 11173, 12391, 12811, 13238, 14561, 15947, 17893, 18397, 19951, 20483, 21568, 22681, 24991, 27413, 29303, 29947, 34651, 37493, 41203, 43513, 46691, 47503, 50821, 54251, 56897, 57793, 65213, 68111, 72073, 76147, 77183, 84631, 89041, 93563, 101746, 102943, 104147, 106576, 110272, 112771, 114031, 115298, 117853, 121738, 123047, 124363, 128353, 129697, 135143, 136522, 139301, 143522, 144943, 146371, 149248, 150697, 152153, 153616, 155086, 158047, 159538, 164053, 168631, 170171, 174833, 176401, 179558, 181147, 184346, 187573, 192466, 194111, 197422, 202441, 204128, 207523, 214397, 216133, 223147, 230273, 235691, 243013, 244861, 252323, 257993, 265651, 267583, 273421, 289297, 297403, 299447, 305621, 307693, 316051, 324521, 333103, 339613, 341797, 357281, 366283, 368551, 384623, 393961, 405791, 415381, 422647, 425083, 432433, 434897, 442331, 465011, 472697, 475273, 485647, 506731, 517441, 528263, 536453, 547471, 569843, 581197, 584053, 592663, 595547, 607153, 627733, 630701, 639647, 654697, 676061, 679141, 688423, 691531, 700897, 726181, 729373, 742211, 748672, 751913, 755161, 764947, 778093, 781397, 808081, 835213, 859321, 873251, 876751, 890821, 901447, 933703, 959183, 973897, 977593, 1003661, 1007413, 1014938, 1018711, 1022491, 1033873, 1037681, 1045318, 1056826, 1064533, 1068397, 1076146, 1080031, 1083923, 1087822, 1095641, 1099561, 1103488, 1115311, 1119266, 1127197, 1131173, 1139146, 1143143, 1151158, 1159201, 1163233, 1175371, 1183498, 1195741, 1203938, 1212163, 1220416, 1228697, 1257901, 1262101, 1274743, 1283206, 1295953, 1304486, 1313047, 1325941, 1330253, 1347571, 1351918, 1369376, 1373758, 1378147, 1382543, 1395773, 1400197, 1409066, 1417963, 1431361, 1444822, 1453831, 1458346, 1467397, 1471933, 1481026, 1490147, 1499296, 1503881, 1508473, 1522291, 1540813, 1545461, 1554778, 1559447, 1578193, 1597051, 1601783, 1620781, 1635103, 1644686, 1654297, 1659113, 1663936, 1673603, 1712551, 1717451, 1732193, 1737121, 1751947, 1756903, 1791791, 1796803, 1806848, 1811881, 1837151, 1867706, 1872823, 1893361, 1919191, 1934773, 1939981, 1955647, 1960883, 1966126, 1976633, 1981897.

Some larger examples :