A056956 Numbers n such that 6n+1 and 6n+5 are both primes.

1, 2, 3, 6, 7, 11, 13, 16, 17, 18, 21, 27, 32, 37, 38, 46, 51, 52, 58, 63, 66, 73, 76, 77, 81, 83, 102, 107, 112, 123, 126, 128, 137, 142, 143, 146, 147, 151, 156, 161, 168, 181, 182, 202, 213, 216, 217, 237, 238, 241, 247, 248, 258, 261, 263, 266, 268, 277, 282

Offset

1,2

Comments

Note that if prime p>3 then p mod 6 = 1 or 5.

Links

M. F. Hasler, Table of n, a(n) for n = 1..5000

Formula

a(n) = (A023200(n+1)-1)/6 = (A046132(n+1)-5)/6 = A047847(n+1)/3

a(n) = floor(A087679(n+1)/6). - M. F. Hasler, Apr 05 2017

Example

a(2)=2 since 6*2+1=13 and 6*2+5=17 are both prime.

Mathematica

Select[Range[300], And @@ PrimeQ /@ ({1, 5} + 6#) &] (* Ray Chandler, Jun 29 2008 *)

Prog

(PARI) is(n)=isprime(n*6+1)&&isprime(n*6+5) \\ M. F. Hasler, Apr 05 2017

Crossrefs

Cf. A002822, A024898, A024899, A059325.

Sequence in context: A113545 A056825 A070757 * A171033 A269983 A323066

Adjacent sequences: A056953 A056954 A056955 * A056957 A056958 A056959

Keyword

nonn

Author

Henry Bottomley, Jul 18 2000

Extensions

Edited by N. J. A. Sloane, Nov 07 2006

Status

approved