A238776 - OEIS

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A238776

Primes p with prime(p) - p + 1 and prime(q) - q + 1 both prime, where q = prime(2*pi(p)+1) with pi(.) given by A000720.

2, 5, 7, 13, 31, 41, 43, 83, 109, 151, 211, 281, 307, 317, 349, 353, 499, 601, 709, 757, 883, 911, 971, 1447, 1453, 1483, 1531, 1801, 2053, 2281, 2819, 2833, 3163, 3329, 3331, 3881, 3907, 4051, 4243, 4447, 4451, 4703, 4751, 5483, 5659, 5701, 5737, 6011, 6271, 6311, 6361, 6379, 6427, 6571, 6827, 6841, 6983, 7159, 7879, 8209

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OFFSET

1,1

COMMENTS

Conjecture: The sequence has infinitely many terms.

This is motivated by the conjecture in A238766. Note that the sequence is a subsequence of A234695.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014.

EXAMPLE

a(1) = 2 since prime(2) - 2 + 1 = 2 and prime(prime(2*pi(2)+1)) - prime(2*pi(2)+1) + 1 = prime(5) - 5 + 1 = 11 - 4 = 7 are both prime.

MATHEMATICA