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%I #13 Jun 28 2017 17:59:18
%S 11,17,43,179,313,353,673,733,809,1021,1481,2333,2371,2473,2741,2767,
%T 4721,4931,5179,5647,5849,6277,7283,7573,8273,8863,8941,8999,9041,
%U 9437,10093,10723,11239,12703,13099,13999,14737,17383,17729,18671,19079,20389,21143,22531
%N Consider two consecutive primes {p,q} such that P=2p+q and Q=2q+p are both prime. The sequence gives primes P.
%e a(1)=11 because p=3, q=5 and P=11 and Q=13 are both prime.
%e a(3)=43 because p=13, q=17 and P=43 and Q=47 are both prime.
%t 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 *)
%t 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 *)
%o (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
%Y Cf. A181848(primes p), A248480(primes q), A248483(primes Q).
%K nonn
%O 1,1
%A _Zak Seidov_, Oct 07 2014
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