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%I #13 Jan 10 2024 12:00:08
%S 13,19,47,181,317,367,677,743,811,1031,1489,2347,2381,2477,2749,2777,
%T 4729,4951,5189,5657,5851,6287,7297,7583,8287,8867,8969,9001,9049,
%U 9463,10103,10733,11261,12713,13109,14009,14747,17393,17749,18679,19081,20399,21157,22541
%N Consider two consecutive primes {p,q} such that P=2p+q and Q=2q+p are both prime. The sequence gives primes Q.
%H Robert Israel, <a href="/A248483/b248483.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1)=13 because p=3, q=5 and P=11 and Q=13 are both prime.
%e a(3)=47 because p=13, q=17 and P=43 and Q=47 are both prime.
%p R:= NULL: count:= 0:
%p q:= 2:
%p while count < 100 do
%p p:= q; q:= nextprime(q);
%p if isprime(2*p+q) and isprime(p+2*q) then
%p count:= count+1; R:= R, p+2*q
%p fi
%p od:
%p R; # _Robert Israel_, Jan 05 2021
%t 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 *)
%t 2#[[2]]+#[[1]]&/@Select[Partition[Prime[Range[1000]],2,1],AllTrue[{2#[[1]]+#[[2]],2#[[2]]+ #[[1]]},PrimeQ]&] (* _Harvey P. Dale_, Jan 10 2024 *)
%o (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
%Y Cf. A181848 (primes p), A248480 (primes q), A248482 (primes P).
%K nonn
%O 1,1
%A _Zak Seidov_, Oct 07 2014
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