A084442 Primes that can be written uniquely as 1+p+p^k, p prime and k>0.

5, 13, 19, 23, 47, 59, 67, 83, 107, 167, 179, 227, 263, 307, 347, 359, 383, 467, 479, 503, 563, 587, 631, 719, 733, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1723, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459