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

Author

Labos Elemer, Nov 28 2000

Keywords

• nonn

Examples

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

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.

Crossrefs

Cf. A101232, A062529, A000230.

Programs

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 *)

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

Formula

a(n) = A000230(3n).

Extensions

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