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%I #8 Apr 14 2021 22:27:14
%S 3,17,31,59,83,97,113,127,131,257,263,379,433,479,491,563,571,619,643,
%T 701,727,811,853,883,919,937,983,1117,1187,1193,1249,1307,1459,1523,
%U 1627,1747,1777,1877,1987,2053,2207,2273,2293,2311,2423,2531,2609,2633,2683,2687,2719,2749,2789,2833,2927
%N Primes p such that 2*p+1+A001414(p+1) is prime.
%C Primes in A343412.
%C 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.
%H Robert Israel, <a href="/A343413/b343413.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 31 is a term because 2*31+1+A001414(31+1) = 73 is prime.
%p filter:= proc(p) local t; isprime(2*p+1+add(t[1]*t[2],t=ifactors(p+1)[2])) end proc:
%p select(filter, map(ithprime, [$1..1000]));
%Y Cf. A001414, A343412.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Apr 14 2021