A078967 Primes p such that the differences between the 5 consecutive primes starting with p are (6,6,4,6).

151, 367, 3307, 4987, 20101, 30097, 52951, 53617, 85831, 92221, 95701, 99817, 103561, 128461, 135601, 163621, 214651, 221071, 241321, 241861, 246907, 274831, 280591, 282691, 287851, 294787, 295831, 297601, 307261, 308311, 334771, 340897, 347161, 350431, 354301

Offset

1,1

Comments

Equivalently, primes p such that p, p+6, p+12, p+16 and p+22 are consecutive primes.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Formula

From Amiram Eldar, Feb 22 2025: (Start)

a(n) == 1 (mod 6).

a(n) == 1 or 7 (mod 30). (End)

Example

151 is in the sequence since 151, 157 = 151 + 6, 163 = 151 + 12, 167 = 151 + 16 and 173 = 151 + 22 are consecutive primes.

Mathematica

Transpose[Select[Partition[Prime[Range[30000]], 5, 1], Differences[#] == {6, 6, 4, 6}&]][[1]] (* Harvey P. Dale, Apr 06 2012 *)

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 == 6, 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: A108842 A078858 A217498 * A089317 A141982 A142271

Adjacent sequences: A078964 A078965 A078966 * A078968 A078969 A078970

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved