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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A103176 A156940 A220162 * A274424 A180528 A109504

Adjacent sequences: A248480 A248481 A248482 * A248484 A248485 A248486

Keyword

nonn

Author

Zak Seidov, Oct 07 2014

Status

approved