A078960 Primes p such that the differences between the 5 consecutive primes starting with p are (6,2,6,6).

593, 4643, 6353, 11483, 19463, 34253, 71333, 77543, 89513, 101273, 135593, 148853, 179813, 184823, 191453, 193373, 245513, 260003, 267893, 277883, 280583, 302573, 307253, 308303, 310223, 344243, 346433, 350423, 376463, 408203, 416393, 435563, 442823, 450473, 482393

Offset: 1

Author

Labos Elemer, Dec 19 2002

Keywords

• nonn

Comments

Equivalently, primes p such that p, p+6, p+8, p+14 and p+20 are consecutive primes.

Examples

			593 is in the sequence since 593, 599 = 593 + 6, 601 = 593 + 8, 607 = 593 + 14 and 613 = 593 + 20 are consecutive primes.
		

Links

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

Crossrefs

Subsequence of A078854. - R. J. Mathar, May 06 2017

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

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[36000]],5,1],Differences[#]=={6,2,6,6}&]][[1]] (* Harvey P. Dale, Oct 14 2013 *)

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 == 6 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 22 2025

Formula

a(n) == 23 (mod 30). - Amiram Eldar, Feb 22 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002