A145471 -id:A145471 - cp's OEIS frontend

A145489 Numbers k such that 6k + 11 is prime and 12k + 5 is also prime.

0, 1, 2, 3, 7, 8, 12, 16, 21, 23, 26, 37, 38, 42, 43, 47, 51, 56, 58, 63, 68, 73, 78, 91, 92, 98, 101, 106, 107, 108, 133, 136, 141, 142, 156, 157, 162, 173, 192, 196, 201, 203, 212, 218, 227, 233, 236, 238, 246, 247, 257, 267, 268, 271, 287, 296, 306, 313, 316, 323, 327, 332, 346, 353, 357, 366, 367, 371, 376, 387, 401, 406, 411, 423, 441, 442, 448, 453, 471, 472, 478, 483, 488, 491, 498

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A063908-A063913, A092109, A145471-A145490.

Select[Range[0,500], PrimeQ[6# + 11 ] && PrimeQ[12# + 5]&]

isok(n) = isprime(6*n+11) && isprime(12*n+5); \\ Michel Marcus, Jan 24 2017

a(n) = (A145475(n) - 5)/12.

Corrected by Artur Jasinski, Apr 01 2011

A274465 Primes which are the sum of cousin prime pairs - 1.

Original entry on oeis.org

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

Debapriyay Mukhopadhyay, Jun 24 2016

nonn

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

			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.

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

Cf. A023200, A152091, A040117, A145471, A089531, A072669.

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

is(n) = isprime(n) && isprime((n-3)/2) && isprime((n+5)/2) \\ David A. Corneth, Jun 24 2016

use ntheory ":all"; say for grep{is_prime($)} map { $+$+4-1 } sieve_prime_cluster(1,5e8,4) # _Dana Jacobsen, Apr 27 2017

cp's OEIS Frontend

A145489 Numbers k such that 6k + 11 is prime and 12k + 5 is also prime.

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