A274506 Primes one less than the sum over a pair of prime numbers that differ by 8.

13, 17, 29, 53, 113, 149, 269, 353, 389, 809, 1193, 1373, 1409, 1493, 1973, 2069, 2129, 2333, 2393, 2753, 2909, 2969, 3209, 4013, 4493, 4673, 5333, 5693, 6029, 6089, 6449, 6653, 7253, 7529, 7829, 7853, 8429, 8513, 9173, 9293, 10889, 10949, 11393, 11489, 11633, 12413, 12713, 12953, 13049, 13313, 14249, 14969

Offset: 1

Author

Debapriyay Mukhopadhyay, Jun 25 2016

Keywords

• nonn

Comments

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

Examples

			13 = 3 + 11 - 1. Note that, (13-7)/2 = 3 and (13+9)/2 = 11 and the prime pairs 3 and 11 differ by 8.
17 = 5 + 13 - 1. Note that, (17-7)/2 = 5 and (17+9)/2 = 13 and the prime pairs 5 and 13 differ by 8.
		

Crossrefs

Cf. A023202, A274507.

Programs

Mathematica

Select[2 Select[Prime@ Range@ 1100, PrimeQ[# + 8] &] + 7, PrimeQ] (* Michael De Vlieger, Jun 26 2016 *)

PARI

lista(nn) = forprime(p=3, nn, if (isprime((p-7)/2) && isprime((p+9)/2), print1(p, ", "));); \\ Michel Marcus, Jun 25 2016

Perl

use ntheory ":all"; say for grep{is_prime($)} map { $+$+8-1 } sieve_prime_cluster(1,5e7,8); # _Dana Jacobsen, Apr 27 2017