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apocalyptic n.  and  brilliant n.

First numbers that belong to both sets:

247, 361, 529, 583, 649, 667, 671, 841, 869, 871, 979, 1081, 1139, 1157, 1219, 1241, 1247, 1261, 1271, 1333, 1343, 1349, 1403, 1411, 1501, 1541, 1591, 1633, 1679, 1739, 1769, 1817, 1829, 1843, 1849, 1891, 2021, 2047, 2059, 2077, 2117, 2231, 2279, 2291, 2407, 2449, 2479, 2491, 2501, 2537, 2581, 2627, 2701, 2809, 2881, 2911, 3007, 3053, 3071, 3139, 3149, 3233, 3239, 3403, 3481, 3551, 3569, 3649, 3713, 3721, 3869, 3901, 3953, 3977, 4087, 4187, 4189, 4331, 4399, 4453, 4559, 4717, 4819, 4897, 5141, 5183, 5251, 5293, 5329, 5429, 5561, 5609, 5723, 5767, 5963, 6059, 6241, 6319, 6497, 6887, 6889, 7031, 7387, 7663, 7921, 8051, 8633, 9409, 10201, 10403, 10609, 10807, 11009, 11021, 11227, 11413, 11449, 11639, 11663, 11881, 12091, 12317, 12769, 12827, 13081, 13231, 13493, 13589, 13837, 13843, 14017, 14039, 14111, 14279, 14317, 14351, 14659, 14803, 14873, 14933, 15049, 15151, 15251, 15347, 15481, 15553, 15707, 15857, 15943, 16129, 16157, 16171, 16241, 16459, 16463, 16637, 16789, 16799, 16837, 16867, 17063, 17113, 17161, 17201, 17399, 17441, 17473, 17653, 17741, 17767, 17819, 17869, 17947, 18079, 18203, 18209, 18281, 18419, 18437, 18511, 18643, 18769, 18857, 18871, 18923, 19043, 19153, 19177, 19291, 19321, 19367, 19493, 19511, 19519, 19549, 19673, 19729, 19781, 19879, 19897, 19939, 20099, 20227, 20291, 20413, 20437, 20453, 20497, 20567, 20651, 20687, 20701, 20711, 20819, 20989, 21037, 21079, 21209, 21293, 21311, 21353, 21473, 21509, 21583, 21691, 21733, 21809, 21823, 21877, 21971, 22201, 22261, 22331, 22487, 22499, 22523, 22577, 22657, 22663, 22733, 22801, 22879, 22927, 22969, 22987, 22999, 23129, 23213, 23381, 23393, 23449, 23533, 23587, 23701, 23707, 23711, 23843, 23861, 23999, 24047, 24139, 24257, 24287, 24289, 24307, 24341, 24503, 24511, 24523, 24613, 24617, 24649, 24743, 24797, 24823, 24881, 24883, 24931, 24961, 25019.

Some larger examples :