A058193 Smallest prime p such that there is a gap of 6n between p and the next prime.

23, 199, 523, 1669, 4297, 9551, 16141, 28229, 35617, 43331, 162143, 31397, 188029, 461717, 404851, 360653, 1444309, 2238823, 492113, 1895359, 1671781, 1357201, 3826019, 11981443, 13626257, 17983717, 39175217, 37305713, 52721113

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..240

Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]

Index entries for primes, gaps between.

Formula

a(n) = A000230(3n).

Example

d = 72 appears after 31397, while smaller d = 54, 60, 66 come later, following primes 35617, 43331, 162143, respectively.

Mathematica

Module[{nn=32*10^5, prs, gps}, prs=Prime[Range[nn]]; gps=Differences[prs]; Table[SelectFirst[Thread[{Most[prs], gps}], #[[2]]==6n&], {n, 30}]][[;; , 1]] (* Harvey P. Dale, Mar 03 2025 *)

Prog

(PARI) a(n) = {p=3; q = nextprime(p+1); while((q-p) != 6*n, p = q; q = nextprime(q+1)); p; } \\ Michel Marcus, Mar 12 2016

Crossrefs

Cf. A101232, A062529, A000230.

Sequence in context: A108646 A307355 A391772 * A065314 A065316 A060882

Adjacent sequences: A058190 A058191 A058192 * A058194 A058195 A058196

Keyword

nonn

Author

Labos Elemer, Nov 28 2000

Extensions

Offset corrected by M. F. Hasler, Apr 09 2013

Status

approved