A139404 Numbers k such that 24*k + 5 and 24*k + 7 are twin primes.

0, 1, 4, 6, 8, 11, 19, 34, 44, 51, 53, 54, 78, 81, 83, 89, 93, 96, 99, 106, 116, 141, 144, 148, 149, 159, 163, 173, 176, 184, 188, 193, 209, 228, 229, 239, 258, 261, 279, 286, 306, 316, 323, 328, 331, 351, 358, 368, 369, 389, 393, 394, 401, 403, 418, 429, 446

Offset: 1

Author

Artur Jasinski, Apr 19 2008

Keywords

• nonn

Comments

1/3 of number k such that 8k + 5 and 8k + 7 are primes.

All numbers in A125821 are divisible by 3.

Examples

			0 is in the sequence since 24*0 + 5 = 5 and 24*0 + 7 = 7 are twin primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A125822, A139402, A139404.

Programs

Magma

[n: n in [0..5000] |IsPrime(24*n+5)and IsPrime(24*n+7)]; // Vincenzo Librandi, Nov 24 2010

Mathematica

a = {}; Do[If[PrimeQ[8 n + 5] && PrimeQ[8 n + 3] && PrimeQ[n],AppendTo[a, n]], {n, 1, 10000}]; a
Select[Range[0,500],AllTrue[24#+{5,7},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 08 2019 *)

Formula

a(n) = A125821(n)/3.

Extensions

a(1) = 0 inserted by Vincenzo Librandi, Mar 25 2010