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A181848 Consider two consecutive primes {p,q} such that P=2p+q and Q=2q+p are both prime. Sequence gives lesser primes p.

%I A181848 #37 Mar 24 2025 16:56:46
%S A181848 3,5,13,59,103,113,223,241,269,337,491,773,787,823,911,919,1571,1637,
%T A181848 1723,1879,1949,2089,2423,2521,2753,2953,2971,2999,3011,3137,3361,
%U A181848 3571,3739,4231,4363,4663,4909,5791,5903,6221,6359,6793,7043,7507,7873,9323,9403
%N A181848 Consider two consecutive primes {p,q} such that P=2p+q and Q=2q+p are both prime. Sequence gives lesser primes p.
%C A181848 Note that Q-P=q-p and {P,Q} are not necessarily consecutive primes.
%H A181848 Zak Seidov, <a href="/A181848/b181848.txt">Table of n, a(n) for n = 1..3000</a>
%e A181848 a(1)=3 because p=3, q=5 and P=11 and Q=13 are both prime
%e A181848 a(3)=13 because p=13, q=17 and P=43 and Q=47 are both prime.
%t A181848 a=2;Reap[Do[b=Prime[n];If[PrimeQ[2*a+b]&&PrimeQ[2*b+a],Sow[a]];a=b,{n,2,200}]][[2,1]]
%t A181848 Select[Partition[Prime[Range[1200]],2,1],AllTrue[{2 #[[1]]+#[[2]],2 #[[2]]+#[[1]]},PrimeQ]&][[;;,1]] (* _Harvey P. Dale_, Mar 24 2025 *)
%o A181848 (PARI) isok(p) = isprime(p) && (q=nextprime(p+1)) && isprime(p+2*q) && isprime(q+2*p); \\ _Michel Marcus_, Mar 05 2016
%Y A181848 Intersection of A173971 and A175914. - _Zak Seidov_, Mar 04 2016
%K A181848 nonn
%O A181848 1,1
%A A181848 _Zak Seidov_, Aug 18 2012