A274507 Primes one more than the sum over a pair of prime numbers that differ by 8.

19, 31, 67, 127, 151, 211, 271, 307, 547, 727, 787, 811, 907, 967, 991, 1447, 1531, 1831, 1867, 2131, 2467, 2647, 2887, 2971, 3967, 5107, 5227, 5407, 5431, 5827, 6091, 6427, 6451, 6607, 6907, 6991, 7411, 8191, 8431, 8707, 9511, 10111

Offset: 1

Author

Debapriyay Mukhopadhyay, Jun 25 2016

Keywords

• nonn

Comments

Any prime p in this sequence is such that p = (p-9)/2 + (p+7)/2 + 1, where (p-9)/2 and (p+7)/2 are also primes and they differ by 8.

This sequence is infinite under Dickson's conjecture. - Charles R Greathouse IV, Jul 08 2016

Examples

			19 = 5 + 13 + 1. Note that, (19-9)/2 = 5 and (19+7)/2 = 13 and the prime pairs 5 and 13 differ by 8.
31 = 11 + 19 + 1. Note that, (31-9)/2 = 11 and (31+7)/2 = 19 and the prime pairs 11 and 19 differ by 8.
		

Crossrefs

Cf. A023202, A274506.

A subsequence of A068229 and also of A145472.

Programs

Mathematica

Select[2 # + 9 &@ Select[Prime@ Range[10^3], PrimeQ[# + 8] &], PrimeQ] (* Michael De Vlieger, Jun 26 2016 *)

PARI

lista(nn)=forprime(p=3, nn, if (isprime(p+8) && isprime(q=2*p+9), print1(q, ", "))); \\ Michel Marcus, Jun 25 2016