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%I #18 Apr 27 2017 23:17:50
%S 13,17,29,53,113,149,269,353,389,809,1193,1373,1409,1493,1973,2069,
%T 2129,2333,2393,2753,2909,2969,3209,4013,4493,4673,5333,5693,6029,
%U 6089,6449,6653,7253,7529,7829,7853,8429,8513,9173,9293,10889,10949,11393,11489,11633,12413,12713,12953,13049,13313,14249,14969
%N Primes one less than the sum over a pair of prime numbers that differ by 8.
%C 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.
%e 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.
%e 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.
%t Select[2 Select[Prime@ Range@ 1100, PrimeQ[# + 8] &] + 7, PrimeQ] (* _Michael De Vlieger_, Jun 26 2016 *)
%o (PARI) lista(nn) = forprime(p=3, nn, if (isprime((p-7)/2) && isprime((p+9)/2), print1(p, ", "));); \\ _Michel Marcus_, Jun 25 2016
%o (Perl) use ntheory ":all"; say for grep{is_prime($_)} map { $_+$_+8-1 } sieve_prime_cluster(1,5e7,8); # _Dana Jacobsen_, Apr 27 2017
%Y Cf. A023202, A274507.
%K nonn
%O 1,1
%A _Debapriyay Mukhopadhyay_, Jun 25 2016