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

Author

Labos Elemer, Dec 19 2002

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

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

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

Programs

Mathematica

Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {6,4,6,6} &][[;;, 1]] (* Amiram Eldar, Feb 22 2025 *)

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

Formula

From Amiram Eldar, Feb 22 2025: (Start)

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

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

Extensions

Edited by Dean Hickerson, Dec 20 2002