A078959 Primes p such that the differences between the 5 consecutive primes starting with p are (6,2,6,4).

23, 53, 263, 1283, 2333, 5843, 6563, 14543, 19373, 32363, 41603, 48473, 49193, 51413, 75983, 88793, 106853, 113153, 115763, 138563, 150203, 160073, 163973, 204353, 223823, 229763, 246923, 284723, 319673, 326993, 337853, 338153, 357653, 433253, 443153, 460073, 460973

Offset

1,1

Comments

Equivalently, primes p such that p, p+6, p+8, p+14 and p+18 are consecutive primes.

Links

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

Formula

a(n) == 23 (mod 30). - Amiram Eldar, Feb 22 2025

Example

53 is a term since 53, 59 = 53 + 6, 61 = 53 + 8, 67 = 53 + 14 and 71 = 53 + 18 are consecutive primes.

Mathematica

l = {}; For[n = 1, n < 10^5, n++, If[Prime[n] + 6 == Prime[n + 1] \[And] Prime[n] + 8 == Prime[n + 2] \[And] Prime[n] + 14 == Prime[n + 3] \[And] Prime[n] + 18 == Prime[n + 4], AppendTo[l, Prime[n]]]]; l (* Jake Foster, Oct 27 2008 *)
Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {6, 2, 6, 4} &][[;; , 1]] (* Amiram Eldar, Feb 22 2025 *)

Prog

(PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 6 && p3 - p2 == 2 && p4 - p3 == 6 && p5 - p4 == 4, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 22 2025

Crossrefs

Subsequence of A078854. - R. J. Mathar, May 06 2017

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

Sequence in context: A051650 A049438 A078854 * A238854 A045345 A133986

Adjacent sequences: A078956 A078957 A078958 * A078960 A078961 A078962

Keyword

nonn,changed

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved