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%I #40 Apr 27 2017 23:17:42
%S 17,29,41,89,137,197,257,389,449,461,557,617,701,761,797,881,929,977,
%T 1229,1289,1481,1709,1721,1877,2609,2861,2897,2969,3137,3221,3329,
%U 3389,3989,4001,4409,4481,4877,5081,5237,5381,5417,5501,5669,5717,6329,6689,6917,7229
%N Primes which are the sum of cousin prime pairs - 1.
%C Cousin primes are prime pairs that differ by 4. Any prime p in this sequence is such that p = (p-3)/2 + (p+5)/2 - 1, where (p-3)/2 and (p+5)/2 are also primes and they differ by 4.
%C Proper subset of A040117 (e.g., 5 isn't in the sequence). - _David A. Corneth_, Jun 24 2016
%C Intersection of A145471 and A089531. - _Michel Marcus_, Jun 27 2016
%C Subsequence of A072669. - _Michel Marcus_, Jun 27 2016
%H John Cerkan, <a href="/A274465/b274465.txt">Table of n, a(n) for n = 1..10000</a>
%e 17 = 7 + 11 - 1. Note that, (17-3)/2 = 7 and (17+5)/2 = 11 and 7, 11 are cousin prime pairs.
%e 29 = 13 + 17 - 1. Note that, (29-3)/2 = 13 and (29+5)/2 = 17 and 13, 17 are cousin prime pairs.
%e 41 = 19 + 23 - 1. Note that, (41-3)/2 = 19 and (41+5)/2 = 23 and 19, 23 are cousin prime pairs.
%e 89 = 43 + 47 - 1. Note that, (89-3)/2 = 43 and (89+5)/2 = 47 and 43, 47 are cousin prime pairs.
%t Select[2 # + 3 &@ Select[Prime@ Range@ 512, PrimeQ[# + 4] &], PrimeQ] (* _Michael De Vlieger_, Jun 26 2016 *)
%o (PARI) is(n) = isprime(n) && isprime((n-3)/2) && isprime((n+5)/2) \\ _David A. Corneth_, Jun 24 2016
%o (Perl) use ntheory ":all"; say for grep{is_prime($_)} map { $_+$_+4-1 } sieve_prime_cluster(1,5e8,4) # _Dana Jacobsen_, Apr 27 2017
%Y Cf. A023200, A152091, A040117, A145471, A089531, A072669.
%K nonn
%O 1,1
%A _Debapriyay Mukhopadhyay_, Jun 24 2016
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