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

3, 5, 13, 59, 103, 113, 223, 241, 269, 337, 491, 773, 787, 823, 911, 919, 1571, 1637, 1723, 1879, 1949, 2089, 2423, 2521, 2753, 2953, 2971, 2999, 3011, 3137, 3361, 3571, 3739, 4231, 4363, 4663, 4909, 5791, 5903, 6221, 6359, 6793, 7043, 7507, 7873, 9323, 9403

Offset: 1

Author

Zak Seidov, Aug 18 2012

Keywords

• nonn

Comments

Note that Q-P=q-p and {P,Q} are not necessarily consecutive primes.

Examples

			a(1)=3 because p=3, q=5 and P=11 and Q=13 are both prime
a(3)=13 because p=13, q=17 and P=43 and Q=47 are both prime.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..3000

Crossrefs

Intersection of A173971 and A175914. - Zak Seidov, Mar 04 2016

Programs

Mathematica

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]]
Select[Partition[Prime[Range[1200]],2,1],AllTrue[{2 #[[1]]+#[[2]],2 #[[2]]+#[[1]]},PrimeQ]&][[;;,1]] (* Harvey P. Dale, Mar 24 2025 *)

PARI

isok(p) = isprime(p) && (q=nextprime(p+1)) && isprime(p+2*q) && isprime(q+2*p); \\ Michel Marcus, Mar 05 2016