A078969 Primes p such that the differences between the 5 consecutive primes starting with p are (6,6,6,4).

3301, 15901, 18211, 30091, 53611, 71341, 77551, 80911, 89101, 120811, 252151, 285451, 292471, 294781, 344251, 601801, 616501, 744811, 792691, 809821, 908521, 912391, 1152631, 1154221, 1279801, 1376491, 1398031, 1455361, 1464271, 1500511, 1503031, 1555111, 1594261

Offset

1,1

Comments

Equivalently, primes p such that p, p+6, p+12, p+18 and p+22 are consecutive primes.

Links

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

Formula

a(n) == 1 (mod 30). - Amiram Eldar, Feb 22 2025

Example

30091 is in the sequence since 30091, 30097 = 30091 + 6, 30103 = 30091 + 12, 30109 = 30091 + 18 and 30113 = 30091 + 22 are consecutive primes.

Mathematica

Select[Partition[Prime[Range[150000]], 5, 1], Differences[#] == {6, 6, 6, 4} &][[;; , 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 == 4, 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: A078951 A236660 A106721 * A320717 A106724 A239671

Adjacent sequences: A078966 A078967 A078968 * A078970 A078971 A078972

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved