A277290 Prime-indexed primes p such that Lucas(p) is prime.
5, 11, 17, 31, 41, 353, 617, 4787, 5851, 148091, 637751
Offset: 1
Examples
17 = A000040(7), with 7 itself being a prime, and A000032(17) = 3571, a prime, thus 17 is included in this sequence.