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A248483 Consider two consecutive primes {p,q} such that P=2p+q and Q=2q+p are both prime. The sequence gives primes Q.

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