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lucky n.  and  weak prime

First numbers that belong to both sets:

3, 7, 13, 31, 43, 73, 151, 193, 241, 283, 349, 409, 421, 433, 463, 577, 601, 619, 643, 823, 883, 997, 1021, 1039, 1093, 1201, 1231, 1291, 1303, 1459, 1723, 1831, 1879, 1933, 2083, 2113, 2221, 2239, 2251, 2311, 2557, 2593, 2689, 2887, 2971, 3049, 3121, 3229, 3259, 3301, 3499, 3559, 3709, 3889, 3931, 4003, 4129, 4363, 4483, 4519, 4567, 4663, 4801, 4969, 5179, 5233, 5419, 5449, 5503, 5641, 5701, 5827, 5851, 5869, 6079, 6229, 6271, 6301, 6379, 6427, 6553, 6661, 6679, 6763, 6841, 6871, 6883, 7129, 7333, 7459, 7489, 7507, 7549, 7591, 7951, 7963, 8089, 8191, 8221, 8233, 8467, 8539, 8647, 8719, 9349, 9403, 9421, 9631, 9649, 9661, 10009, 10069, 10111, 10321, 10399, 10459, 10501, 10531, 10753, 10789, 10891, 10909, 11059, 11173, 11491, 11833, 11959, 12049, 12163, 12301, 12379, 12457, 12553, 12589, 12763, 12799, 13009, 13063, 13219, 13267, 13537, 13633, 13681, 13693, 13723, 13759, 13831, 14347, 14437, 14449, 14461, 14797, 15031, 15271, 15511, 16381, 16573, 16747, 16981, 17053, 17209, 17341, 17359, 17389, 17401, 17497, 17581, 17713, 17737, 17749, 18043, 18049, 18253, 18523, 18757, 18979, 19051, 19081, 19237, 19309, 19333, 19543, 19609, 19687, 19963, 19993, 20071, 20149, 20359, 20509, 20551, 20563, 20611, 20773, 20887, 20899, 21013, 21169, 21193, 21433, 21529, 21613, 21739, 21757, 21841, 22039, 22093, 22369, 22651, 22921, 23041, 23173, 23293, 23563, 23671, 23677, 23689, 23929, 24121, 24151, 24181, 24481, 24571, 24709, 25033, 25153, 25171, 25189, 25309, 25771, 25819, 26119, 26209, 26251, 26263, 26347, 26683, 26881, 26893, 27061, 27283, 27409, 27457, 27541, 27691, 27751, 27793, 28087, 28123, 28351, 28393, 28759, 28771, 28843, 28933, 29137, 29311, 29611, 29959, 29989, 30013, 30367, 30559, 30727, 30817, 30871, 30949, 31039, 31069, 31081, 31237, 31249, 31489, 31573, 31699, 31723, 31849, 32119, 32533, 32563.

Some larger examples :