A078958 Primes p such that the differences between the 5 consecutive primes starting with p are (6,2,4,6).

1601, 3911, 12101, 14621, 32051, 68891, 122021, 191441, 258101, 259151, 276581, 278801, 305471, 347051, 390101, 394721, 418331, 419591, 421691, 470201, 482501, 509681, 678641, 683471, 832361, 844421, 914351, 929051, 977351, 997091, 1043831, 1074701, 1104731, 1224851

Offset

1,1

Comments

Equivalently, primes p such that p, p+6, p+8, 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 22 2025

Example

3911 is in the sequence since 3911, 3917 = 3911 + 6, 3919 = 3911 + 8, 3923 = 3911 + 12 and 3929 = 3911 + 18 are consecutive primes.

Mathematica

Select[Partition[Prime[Range[82000]], 5, 1], Differences[#]=={6, 2, 4, 6}&][[All, 1]] (* Harvey P. Dale, Jul 09 2021 *)

Prog

(PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 6 && p3 - p2 == 2 && p4 - p3 == 4 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 22 2025

Crossrefs

Subsequence of A078853. - R. J. Mathar, May 06 2017

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

Sequence in context: A279241 A060566 A078853 * A031758 A154505 A031538

Adjacent sequences: A078955 A078956 A078957 * A078959 A078960 A078961

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved