

A274506


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


1



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
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OFFSET

1,1


COMMENTS

Any prime p in this sequence is such that p = (p7)/2 + (p+9)/2  1, where (p7)/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, (137)/2 = 3 and (13+9)/2 = 11 and the prime pairs 3 and 11 differ by 8.
17 = 5 + 13  1. Note that, (177)/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((p7)/2) && isprime((p+9)/2), print1(p, ", ")); ); \\ Michel Marcus, Jun 25 2016
(Perl) use ntheory ":all"; say for grep{is_prime($_)} map { $_+$_+81 } 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



