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

Offset: 1

Author

Zhi-Wei Sun, Mar 05 2014

Keywords

• nonn

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.

Examples

			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.
		

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.

Crossrefs

Cf. A000040, A000720, A234695, A238766.

Programs

Mathematica

p[k_]:=PrimeQ[Prime[Prime[k]]-Prime[k]+1]
n=0;Do[If[p[k]&&p[2k+1],n=n+1;Print[n," ",Prime[k]]],{k,1,1029}]