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

1,1

Links

Table of n, a(n) for n=1..44.

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A190800 A191456 A146036 * A267772 A046122 A217064

Adjacent sequences: A248479 A248480 A248481 * A248483 A248484 A248485

Keyword

nonn

Author

Zak Seidov, Oct 07 2014

Status

approved