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

1,1

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

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

Sequence in context: A233823 A142084 A140850 * A186169 A142119 A358399

Adjacent sequences: A078962 A078963 A078964 * A078966 A078967 A078968

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved