A242746 - OEIS

%I #11 Mar 13 2020 10:42:15

%S 1,1,3,1,4,1,5,3,6,1,7,1,7,6,5,1,7,1,5,4,7,1,7,6,4,9,8,1,7,1,9,8,7,6,

%T 5,1,8,7,6,1,7,1,11,10,9,1,9,8,7,10,9,1,7,6,5,7,13,1,11,1,9,8,7,8,7,1,

%U 13,12,11,1,9,1,7,6,8,8,7,1,11,10,9,1,7,6,11,10,9,1,11

%N Least k > 0 such that (k!+n!)/(k+n) is an integer.

%C a(n) = 1 iff n+1 is prime.

%H Harvey P. Dale, <a href="/A242746/b242746.txt">Table of n, a(n) for n = 1..1000</a>

%e (1!+3!)/(1+3) = 7/4 is not an integer. (2!+3!)/(2+3) = 8/5 is not an integer. (3!+3!)/(3+3) = 12/6 = 2 is an integer. Thus a(3) = 3.

%t lnk[n_]:=Module[{k=1,nf=n!},While[!IntegerQ[(k!+nf)/(k+n)],k++];k]; Array[ lnk,90] (* _Harvey P. Dale_, Sep 26 2014 *)

%o (PARI) a(n) = for(k=1, oo, if((k!+n!)%(k+n)==0, return(k))); \\ Modified by _Jinyuan Wang_, Mar 13 2020

%K nonn

%O 1,3

%A _Derek Orr_, May 21 2014