A248483 Consider two consecutive primes {p,q} such that P=2p+q and Q=2q+p are both prime. The sequence gives primes Q.

13, 19, 47, 181, 317, 367, 677, 743, 811, 1031, 1489, 2347, 2381, 2477, 2749, 2777, 4729, 4951, 5189, 5657, 5851, 6287, 7297, 7583, 8287, 8867, 8969, 9001, 9049, 9463, 10103, 10733, 11261, 12713, 13109, 14009, 14747, 17393, 17749, 18679, 19081, 20399, 21157, 22541

Offset: 1

Author

Zak Seidov, Oct 07 2014

Keywords

• nonn

Examples

			a(1)=13 because p=3, q=5 and P=11 and Q=13 are both prime.
a(3)=47 because p=13, q=17 and P=43 and Q=47 are both prime.
		

Links

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

Crossrefs

Cf. A181848 (primes p), A248480 (primes q), A248482 (primes P).

Programs

Maple

R:= NULL: count:= 0:
q:= 2:
while count < 100 do
  p:= q; q:= nextprime(q);
  if isprime(2*p+q) and isprime(p+2*q) then
    count:= count+1; R:= R, p+2*q
  fi
od:
R; # Robert Israel, Jan 05 2021

Mathematica

Select[Table[If[PrimeQ[2*Prime[j-1] + Prime[j]] && PrimeQ[Prime[j-1] + 2*Prime[j]],Prime[j-1] + 2*Prime[j],0],{j,2,2000}],#!=0&] (* Vaclav Kotesovec, Oct 08 2014 *)
2#[[2]]+#[[1]]&/@Select[Partition[Prime[Range[1000]],2,1],AllTrue[{2#[[1]]+#[[2]],2#[[2]]+ #[[1]]},PrimeQ]&]  (* Harvey P. Dale, Jan 10 2024 *)

PARI

listQ(nn) = {forprime(p=2, nn, q = nextprime(p+1); if (isprime(2*p+q) && isprime(Q=2*q+p), print1(Q, ", ")););} \\ Michel Marcus, Oct 07 2014