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

1,1

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

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}]

Crossrefs

Cf. A000040, A000720, A234695, A238766.

Sequence in context: A038945 A215210 A177997 * A141112 A053647 A023242

Adjacent sequences: A238773 A238774 A238775 * A238777 A238778 A238779

Keyword

nonn

Author

Zhi-Wei Sun, Mar 05 2014

Status

approved