

A274465


Primes which are the sum of cousin prime pairs  1.


1



17, 29, 41, 89, 137, 197, 257, 389, 449, 461, 557, 617, 701, 761, 797, 881, 929, 977, 1229, 1289, 1481, 1709, 1721, 1877, 2609, 2861, 2897, 2969, 3137, 3221, 3329, 3389, 3989, 4001, 4409, 4481, 4877, 5081, 5237, 5381, 5417, 5501, 5669, 5717, 6329, 6689, 6917, 7229
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OFFSET

1,1


COMMENTS

Cousin primes are prime pairs that differ by 4. Any prime p in this sequence is such that p = (p3)/2 + (p+5)/2  1, where (p3)/2 and (p+5)/2 are also primes and they differ by 4.
Proper subset of A040117 (e.g., 5 isn't in the sequence).  David A. Corneth, Jun 24 2016
Intersection of A145471 and A089531.  Michel Marcus, Jun 27 2016
Subsequence of A072669.  Michel Marcus, Jun 27 2016


LINKS

John Cerkan, Table of n, a(n) for n = 1..10000


EXAMPLE

17 = 7 + 11  1. Note that, (173)/2 = 7 and (17+5)/2 = 11 and 7, 11 are cousin prime pairs.
29 = 13 + 17  1. Note that, (293)/2 = 13 and (29+5)/2 = 17 and 13, 17 are cousin prime pairs.
41 = 19 + 23  1. Note that, (413)/2 = 19 and (41+5)/2 = 23 and 19, 23 are cousin prime pairs.
89 = 43 + 47  1. Note that, (893)/2 = 43 and (89+5)/2 = 47 and 43, 47 are cousin prime pairs.


MATHEMATICA

Select[2 # + 3 &@ Select[Prime@ Range@ 512, PrimeQ[# + 4] &], PrimeQ] (* Michael De Vlieger, Jun 26 2016 *)


PROG

(PARI) is(n) = isprime(n) && isprime((n3)/2) && isprime((n+5)/2) \\ David A. Corneth, Jun 24 2016
(Perl) use ntheory ":all"; say for grep{is_prime($_)} map { $_+$_+41 } sieve_prime_cluster(1, 5e8, 4) # Dana Jacobsen, Apr 27 2017


CROSSREFS

Cf. A023200, A152091, A040117, A145471, A089531, A072669.
Sequence in context: A096785 A104228 A049484 * A110573 A190497 A259614
Adjacent sequences: A274462 A274463 A274464 * A274466 A274467 A274468


KEYWORD

nonn


AUTHOR

Debapriyay Mukhopadhyay, Jun 24 2016


STATUS

approved



