A078949 Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,4,6).

71, 431, 2339, 2381, 5849, 6959, 27791, 32561, 41609, 45119, 46439, 48479, 51419, 54401, 63599, 78779, 81551, 106859, 115319, 130631, 138569, 143501, 153269, 166601, 183569, 196169, 204359, 229751, 246929, 266081, 279119, 321311, 326999, 350729, 357659, 362741

Offset: 1

Author

Labos Elemer, Dec 19 2002

Keywords

• nonn

Comments

Equivalently, primes p such that p, p+2, p+8, p+12 and p+18 are consecutive primes.

Examples

			71 is in the sequence since 71, 73 = 71 + 2, 79 = 71 + 8, 83 = 71 + 12 and 89 = 71 + 18 are consecutive primes.
		

Links

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

Crossrefs

Subsequence of A078848. - R. J. Mathar, Feb 10 2013

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

Programs

Mathematica

Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {2, 6, 4, 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 == 4 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 21 2025

Formula

From Amiram Eldar, Feb 21 2025: (Start)

a(n) == 5 (mod 6).

a(n) == 11 or 29 (mod 30). (End)

Extensions

Edited by Dean Hickerson, Dec 20 2002