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de Polignac n.  and  Duffinian n.

First numbers that belong to both sets:

905, 959, 1207, 1211, 1243, 1271, 1477, 1529, 1541, 1589, 1649, 1807, 1829, 1859, 1927, 1969, 1985, 2171, 2231, 2263, 2279, 2429, 2669, 2983, 2993, 3149, 3215, 3239, 3341, 3353, 3431, 3505, 3665, 3817, 3985, 4063, 4151, 4503, 4543, 4573, 4589, 4633, 4717, 4781, 4811, 4841, 4843, 4855, 5125, 5143, 5405, 5467, 5609, 5617, 5729, 5731, 5755, 5761, 5771, 5917, 5951, 6001, 6021, 6065, 6119, 6161, 6193, 6283, 6403, 6433, 6463, 6509, 6535, 6539, 6731, 6757, 6821, 6853, 6941, 7169, 7199, 7267, 7289, 7319, 7379, 7387, 7405, 7535, 7747, 7783, 7799, 7807, 7811, 7813, 7913, 7961, 8023, 8031, 8107, 8141, 8159, 8257, 8399, 8411, 8587, 8621, 8789, 8873, 8915, 8921, 8981, 9101, 9115, 9307, 9457, 9517, 9557, 9569, 9581, 9641, 9959, 10001, 10021, 10027, 10121, 10199, 10237, 10327, 10379, 10409, 10447, 10451, 10483, 10511, 10553, 10697, 10777, 10873, 10963, 11015, 11023, 11081, 11105, 11137, 11207, 11219, 11227, 11231, 11285, 11335, 11347, 11435, 11541, 11627, 11729, 11771, 11857, 11993, 12131, 12191, 12223, 12233, 12371, 12427, 12431, 12727, 12731, 12733, 12749, 12805, 12877, 12881, 13091, 13285, 13351, 13393, 13409, 13589, 13603, 13735, 13897, 13961, 13973, 14021, 14023, 14039, 14047, 14077, 14101, 14141, 14227, 14231, 14279, 14375, 14381, 14383, 14459, 14467, 14473, 14531, 14585, 14605, 14611, 14681, 14765, 14809, 14917, 14921, 14981, 15037, 15041, 15059, 15071, 15113, 15119, 15127, 15223, 15247, 15419, 15521, 15701, 15779, 15853, 15943, 15997, 16013, 16025, 16027, 16031, 16109, 16117, 16165, 16177, 16181, 16213, 16405, 16409, 16499, 16507, 16543, 16559, 16601, 16727, 16739, 16753, 16783, 16865, 16867, 16973, 17039, 17083, 17089, 17113, 17147, 17229, 17269, 17305, 17369, 17371, 17411, 17429, 17437, 17557, 17593, 17651, 17735, 17759, 17767, 17773, 17849, 17861, 17887, 18103, 18155, 18209, 18359, 18391, 18551, 18607, 18611.

Some larger examples :