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Smallest prime p such that there is a gap of 6n between p and the next prime.
5

%I #13 Oct 28 2021 12:37:08

%S 23,199,523,1669,4297,9551,16141,28229,35617,43331,162143,31397,

%T 188029,461717,404851,360653,1444309,2238823,492113,1895359,1671781,

%U 1357201,3826019,11981443,13626257,17983717,39175217,37305713,52721113

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

%H Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a> [For local copy see A000101]

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>.

%F a(n) = A000230(3n).

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

%o (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

%Y Cf. A101232, A062529, A000230.

%K nonn

%O 1,1

%A _Labos Elemer_, Nov 28 2000

%E Offset corrected by _M. F. Hasler_, Apr 09 2013