A248482 Consider two consecutive primes {p,q} such that P=2p+q and Q=2q+p are both prime. The sequence gives primes P.

11, 17, 43, 179, 313, 353, 673, 733, 809, 1021, 1481, 2333, 2371, 2473, 2741, 2767, 4721, 4931, 5179, 5647, 5849, 6277, 7283, 7573, 8273, 8863, 8941, 8999, 9041, 9437, 10093, 10723, 11239, 12703, 13099, 13999, 14737, 17383, 17729, 18671, 19079, 20389, 21143, 22531

Offset: 1

Author

Zak Seidov, Oct 07 2014

Keywords

• nonn

Examples

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

Crossrefs

Cf. A181848(primes p), A248480(primes q), A248483(primes Q).

Programs

Mathematica

Select[Table[If[PrimeQ[2*Prime[j-1] + Prime[j]] && PrimeQ[Prime[j-1] + 2*Prime[j]],2*Prime[j-1] + Prime[j],0],{j,2,2000}],#!=0&] (* Vaclav Kotesovec, Oct 08 2014 *)
2#[[1]]+#[[2]]&/@Select[Partition[Prime[Range[1000]],2,1],AllTrue[ {2#[[1]]+ #[[2]],2#[[2]]+#[[1]]},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 28 2017 *)

PARI

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