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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 28 21:04 EDT 2022. Contains 354907 sequences. (Running on oeis4.)