A078953 Primes p such that the differences between the 5 consecutive primes starting with p are (4,2,6,4).

67, 2377, 21487, 31177, 65167, 67927, 81547, 139297, 166597, 178597, 185527, 305017, 305407, 321817, 341947, 390487, 427417, 448867, 547357, 600877, 635347, 668527, 693727, 697507, 752287, 764887, 783787, 812347, 819487, 877867, 1196857, 1229197, 1262617, 1279177

Offset: 1

Author

Labos Elemer, Dec 19 2002

Keywords

• nonn

Comments

Equivalently, primes p such that p, p+4, p+6, p+12 and p+16 are consecutive primes.

Examples

			67 is in the sequence since 67, 71 = 67 + 4, 73 = 67 + 6, 79 = 67 + 12 and 83 = 67 + 16 are consecutive primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from R. J. Mathar)

Crossrefs

Subsequence of A078850. - R. J. Mathar, Feb 11 2013

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

Programs

Mathematica

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

Formula

a(n) == 7 (mod 30). - Amiram Eldar, Feb 21 2025

Extensions

Edited by Dean Hickerson, Dec 20 2002