A343413 Primes p such that 2*p+1+A001414(p+1) is prime.

3, 17, 31, 59, 83, 97, 113, 127, 131, 257, 263, 379, 433, 479, 491, 563, 571, 619, 643, 701, 727, 811, 853, 883, 919, 937, 983, 1117, 1187, 1193, 1249, 1307, 1459, 1523, 1627, 1747, 1777, 1877, 1987, 2053, 2207, 2273, 2293, 2311, 2423, 2531, 2609, 2633, 2683, 2687, 2719, 2749, 2789, 2833, 2927

Offset

1,1

Comments

Primes in A343412.

Includes 6*q-1 where q, 6*q-1 and 13*q+4 are prime; Dickson's conjecture implies there are infinitely many such q.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 31 is a term because 2*31+1+A001414(31+1) = 73 is prime.

Maple

filter:= proc(p) local t; isprime(2*p+1+add(t[1]*t[2], t=ifactors(p+1)[2])) end proc:
select(filter, map(ithprime, [$1..1000]));

Crossrefs

Cf. A001414, A343412.

Sequence in context: A365234 A377175 A045437 * A321796 A372797 A214093

Adjacent sequences: A343410 A343411 A343412 * A343414 A343415 A343416

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Apr 14 2021

Status

approved