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

1,1

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.

Links

Table of n, a(n) for n=1..52.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A023202, A274507.

Sequence in context: A283407 A283358 A033210 * A107159 A138375 A180526

Adjacent sequences: A274503 A274504 A274505 * A274507 A274508 A274509

Keyword

nonn

Author

Debapriyay Mukhopadhyay, Jun 25 2016

Status

approved