A240622 - OEIS

%I #16 Mar 31 2020 03:44:55

%S 3,3,4,4,5,4,7,4,6,5,15,6,13,7,5,9,38,8,21,5,7,19,27,6,15,14,10,7,30,

%T 5,31,8,12,18,8,6,47,53,13,5,127,10,67,11,16,27,51,8,14,26,17,16,77,9,

%U 23,7,184,56,123,6,66,203,7,9,13,13,74,42,26,7,75,9,205

%N Least number k such that k!/n - 1 is prime.

%C a(263) > 5000. - _Jinyuan Wang_, Mar 31 2020

%H Jinyuan Wang, <a href="/A240622/b240622.txt">Table of n, a(n) for n = 1..262</a>

%e 1!/1 - 1 = 0 is not prime. 2!/1 - 1 = 1 is not prime. 3!/1 - 1 = 5 is prime. Thus, a(1) = 3.

%t lnk[n_]:=Module[{k=1},While[!PrimeQ[k!/n-1],k++];k]; Array[lnk,80] (* _Harvey P. Dale_, Aug 31 2015 *)

%o (PARI) a(n) = {for(k=1, oo, s=k!/n-1; if(floor(s)==s, if(ispseudoprime(s), return(k)))); }

%Y Cf. A139072, A139186.

%K nonn

%O 1,1

%A _Derek Orr_, Apr 09 2014