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Friedman n.  and  prime n.

First numbers that belong to both sets:

127, 347, 2503, 12101, 12107, 12109, 15629, 15641, 15661, 15667, 15679, 16381, 16447, 16759, 16879, 19739, 21943, 27653, 28547, 28559, 29527, 29531, 32771, 32783, 35933, 36457, 39313, 39343, 43691, 45361, 46619, 46633, 46643, 46649, 46663, 46691, 48751, 48757, 49277, 58921, 59051, 59053, 59263, 59273, 64513, 74353, 74897, 78163, 83357, 102497, 103681, 103687, 104879, 108233, 109357, 114377, 114679, 115249, 116827, 117571, 117577, 117619, 117643, 117659, 117673, 117763, 118259, 118543, 118673, 122503, 124991, 125003, 125017, 125029, 125053, 125063, 125093, 126397, 127453, 127583, 127649, 128153, 129607, 131071, 131749, 132499, 132527, 132647, 132679, 132859, 137623, 137791, 139967, 139969, 140629, 143357, 146417, 147397, 147419, 147449, 147457, 151273, 151279, 151379, 153649, 156127, 156217, 156227, 156241, 156253, 156257, 156259, 157393, 157457, 157639, 160243, 161047, 161053, 161059, 163841, 163847, 165247, 166393, 176699, 177383, 179327, 181243, 186569, 186619, 186629, 186649, 186653, 187277, 194471, 194483, 194521, 194723, 195311, 196543, 196687, 205391, 205399, 207953, 209953, 215983, 216023, 216037, 216061, 216071, 216091, 218453, 221849, 225619, 227467, 229373, 231367, 234259, 234281, 234287, 234383, 234473, 234571, 235273, 235673, 236219, 237691, 238331, 238363, 241663, 242059, 244379, 245753, 245963, 246793, 247069, 247099, 247301, 248593, 248783, 248839, 249853, 249973, 250007, 250013, 250027, 250031, 250037, 250043, 250049, 250051, 250057, 250073, 250091, 253013, 253273, 254369, 256049, 259099, 259201, 259841, 261529, 261823, 261887, 262079, 262127, 262133, 262139, 262147, 262151, 262153, 262187, 262313, 262369, 262387, 263443, 264331, 265231, 265619, 265729, 265739, 268757, 268759, 273521, 274583, 274627, 276673, 278479, 278651, 279443, 279641, 279761, 279767, 279847, 279857, 279863, 279941, 279967, 285721, 285749, 285763, 286493, 287503, 287681, 287689, 289453, 290531, 294829, 294887, 294911, 295237, 295247, 295259, 295283, 300733, 311473, 312743, 314569, 314927, 319489, 323369, 326561, 326567, 326597, 326617, 326657, 326951, 328051, 328511, 328513, 328519, 328543, 331769, 343037, 343087, 344611, 345739, 345749, 345869, 347359, 352483.

Some larger examples :