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

1,1

Comments

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

Links

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

Formula

From Amiram Eldar, Feb 21 2025: (Start)

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

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

Example

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

Mathematica

Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {2, 6, 4, 6} &][[;; , 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 == 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

Crossrefs

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

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

Sequence in context: A297846 A142304 A201313 * A057541 A268889 A142432

Adjacent sequences: A078946 A078947 A078948 * A078950 A078951 A078952

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved