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

1,1

Comments

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

Links

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

Formula

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

Example

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

Mathematica

Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {4, 2, 6, 4} &][[;; , 1]] (* Amiram Eldar, Feb 21 2025 *)

Prog

(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

Crossrefs

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

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

Sequence in context: A092795 A017783 A017730 * A226713 A069397 A393191

Adjacent sequences: A078950 A078951 A078952 * A078954 A078955 A078956

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved