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

1,1

Comments

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

Links

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

Example

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.

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]]

Prog

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

Crossrefs

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

Sequence in context: A276827 A034375 A081953 * A243161 A153207 A144718

Adjacent sequences: A181845 A181846 A181847 * A181849 A181850 A181851

Keyword

nonn

Author

Zak Seidov, Aug 18 2012

Status

approved