A274465 Primes which are the sum of cousin prime pairs - 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

Offset

1,1

Comments

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.

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, (17-3)/2 = 7 and (17+5)/2 = 11 and 7, 11 are cousin prime pairs.
29 = 13 + 17 - 1. Note that, (29-3)/2 = 13 and (29+5)/2 = 17 and 13, 17 are cousin prime pairs.
41 = 19 + 23 - 1. Note that, (41-3)/2 = 19 and (41+5)/2 = 23 and 19, 23 are cousin prime pairs.
89 = 43 + 47 - 1. Note that, (89-3)/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((n-3)/2) && isprime((n+5)/2) \\ David A. Corneth, Jun 24 2016
(Perl) use ntheory ":all"; say for grep{is_prime($_)} map { $_+$_+4-1 } 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