A078965 Primes p such that the differences between the 5 consecutive primes starting with p are (6,6,2,6).

47, 257, 557, 587, 1217, 4007, 6257, 10847, 14537, 17477, 19457, 26717, 41597, 51407, 84047, 94427, 101267, 115757, 131927, 150077, 150197, 154067, 169307, 179807, 185057, 193367, 206807, 250037, 267887, 275147, 290027, 302567, 344237, 408197, 428027, 442817, 443147

Offset: 1

Author

Labos Elemer, Dec 19 2002

Keywords

• nonn

Comments

Equivalently, primes p such that p, p+6, p+12, p+14 and p+20 are consecutive primes.

Examples

			257 is in the sequence since 257, 263 = 257 + 6, 269 = 257 + 12, 271 = 257 + 14 and 277 = 257 + 20 are consecutive primes.
		

Links

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

Crossrefs

Subsequence of A078857. - R. J. Mathar, May 06 2017

Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Programs

Mathematica

Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {6,6,2,6} &][[;;, 1]] (* Amiram Eldar, Feb 22 2025 *)

PARI

list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 6 && p3 - p2 == 6 && p4 - p3 == 2 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 22 2025

Formula

a(n) == 17 (mod 30). - Amiram Eldar, Feb 22 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002