A078966 Primes p such that the differences between the 5 consecutive primes starting with p are (6,6,4,2).

601, 2671, 20341, 24091, 41941, 42391, 55201, 65701, 87541, 125101, 198811, 249421, 355501, 414691, 416401, 428551, 510061, 521161, 541531, 543871, 560221, 603901, 609601, 637711, 663961, 669661, 743161, 770041, 986131, 1020961, 1026661, 1099711, 1113181, 1120501

Offset

1,1

Comments

Equivalently, primes p such that p, p+6, p+12, p+16 and p+18 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

601 is in the sequence since 601, 607 = 601 + 6, 613 = 601 + 12, 617 = 601 + 16 and 619 = 601 + 18 are consecutive primes.

Mathematica

Transpose[Select[Partition[Prime[Range[81000]], 5, 1], Differences[#] == {6, 6, 4, 2}&]][[1]] (* Harvey P. Dale, Sep 15 2011 *)

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 == 4 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 22 2025

Crossrefs

Subsequence of A078858. - R. J. Mathar, May 06 2017

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

Sequence in context: A050202 A031422 A359638 * A255024 A362323 A283923

Adjacent sequences: A078963 A078964 A078965 * A078967 A078968 A078969

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved