

A274507


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


1



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
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OFFSET

1,1


COMMENTS

Any prime p in this sequence is such that p = (p9)/2 + (p+7)/2 + 1, where (p9)/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, (199)/2 = 5 and (19+7)/2 = 13 and the prime pairs 5 and 13 differ by 8.
31 = 11 + 19 + 1. Note that, (319)/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



