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

1,1

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

Links

Table of n, a(n) for n=1..42.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A023202, A274506.

A subsequence of A068229 and also of A145472.

Sequence in context: A141184 A033212 A104227 * A032743 A106861 A107168

Adjacent sequences: A274504 A274505 A274506 * A274508 A274509 A274510

Keyword

nonn

Author

Debapriyay Mukhopadhyay, Jun 25 2016

Status

approved