A078964 Primes p such that the differences between the 5 consecutive primes starting with p are (6,4,6,6).

157, 4441, 6961, 8731, 14731, 16411, 16921, 20107, 25447, 39097, 47287, 47491, 60601, 78157, 78781, 84121, 92347, 104701, 114067, 115321, 128467, 142537, 183571, 186097, 194707, 196171, 253417, 279121, 286477, 297607, 307267, 327001, 350437, 351031, 354307, 357661

Offset

1,1

Comments

Equivalently, primes p such that p, p+6, p+10, p+16 and p+22 are consecutive primes.

Links

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

Formula

From Amiram Eldar, Feb 22 2025: (Start)

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

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

Example

157 is in the sequence since 157, 163 = 157 + 6, 167 = 157 + 10, 173 = 157 + 16 and 179 = 157 + 22 are consecutive primes.

Mathematica

Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {6, 4, 6, 6} &][[;; , 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 == 4 && p4 - p3 == 6 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 22 2025

Crossrefs

Subsequence of A078856. - R. J. Mathar, May 06 2017

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

Sequence in context: A167992 A038493 A212237 * A171345 A327849 A066823

Adjacent sequences: A078961 A078962 A078963 * A078965 A078966 A078967

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved