A078968 Primes p such that the differences between the 5 consecutive primes starting with p are (6,6,6,2).

251, 17471, 56081, 75521, 94421, 115751, 121001, 154061, 163841, 179801, 185051, 250031, 344231, 351041, 380441, 417941, 517061, 683681, 703211, 713171, 783131, 849581, 916451, 983771, 1003091, 1025261, 1055591, 1070411, 1115561, 1129841, 1260881, 1517921, 1565171

Offset

1,1

Comments

Equivalently, primes p such that p, p+6, p+12, p+18 and p+20 are consecutive primes.

Links

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

Formula

a(n) == 11 (mod 30). - Amiram Eldar, Feb 22 2025

Example

251 is in the sequence since 251, 257 = 251 + 6, 263 = 251 + 12, 269 = 251 + 18 and 271 = 251 + 20 are consecutive primes.

Mathematica

Select[Partition[Prime[Range[150000]], 5, 1], Differences[#] == {6, 6, 6, 2} &][[;; , 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 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 22 2025

Crossrefs

Subsequence of A033451. - R. J. Mathar, May 06 2017

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

Sequence in context: A234929 A218639 A090834 * A365468 A052239 A089236

Adjacent sequences: A078965 A078966 A078967 * A078969 A078970 A078971

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved