A078947 Primes p such that the differences between the 5 consecutive primes starting with p are (2,4,6,6).

41, 641, 1091, 4001, 9461, 26681, 26711, 44531, 79811, 103991, 110921, 112571, 172421, 223241, 276821, 289841, 290021, 317771, 373181, 381371, 434921, 450881, 493121, 602081, 678761, 788351, 834131, 907211, 974861, 1076501, 1081121, 1097891, 1200371, 1409531, 1426151

Offset

1,1

Comments

Equivalently, primes p such that p, p+2, p+6, p+12 and p+18 are consecutive primes.

Links

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

Formula

a(n) == 11 (mod 30). - Amiram Eldar, Feb 21 2025

Example

641 is in the sequence since 641, 643 = 641 + 2, 647 = 641 + 6, 653 = 641 + 12 and 659 = 641 + 18 are consecutive primes.

Mathematica

Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {2, 4, 6, 6} &][[;; , 1]] (* Amiram Eldar, Feb 21 2025 *)

Prog

(PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 2 && p3 - p2 == 4 && p4 - p3 == 6 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 21 2025

Crossrefs

Subsequence of A078847.

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

Sequence in context: A241622 A276251 A298627 * A299600 A197371 A268748

Adjacent sequences: A078944 A078945 A078946 * A078948 A078949 A078950

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved