A078951 Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,6,6).

3299, 5099, 6359, 19469, 30089, 53609, 63689, 71339, 77549, 80909, 105359, 119549, 152939, 186869, 292469, 302969, 344249, 348239, 408209, 415949, 652739, 707669, 737039, 792689, 818339, 831539, 852749, 886979, 910199, 974969, 1072829, 1152629, 1290629, 1368329

Offset: 1

Author

Labos Elemer, Dec 19 2002

Keywords

• nonn

Comments

Equivalently, primes p such that p, p+2, p+8, p+14 and p+20 are consecutive primes.

Examples

			5099 is in the sequence since 5099, 5101 = 5099 + 2, 5107 = 5099 + 8, 5113 = 5099 + 14 and 5119 = 5099 + 20 are consecutive primes.
		

Links

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

Crossrefs

Subsequence of A078849. - R. J. Mathar, May 06 2017

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

Programs

Mathematica

Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {2, 6, 6, 6} &][[;;, 1]] (* Amiram Eldar, Feb 21 2025 *)

PARI

list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 2 && p3 - p2 == 6 && p4 - p3 == 6 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

a(n) == 29 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002