%I #20 Jul 27 2020 04:44:58
%S 0,0,1,2,2,1,2,3,3,0,3,1,3,1,2,0,3,1,3,1,2,0,3,1,3,4,4,0,4,1,4,1,2,0,
%T 4,0,4,1,2,0,4,1,4,1,2,0,4,1,3,0,0,0,4,1,4,0,0,0,3,1,4,1,2,0,4,0,4,1,
%U 2,0,4,1,3,1,2,0,4,0,3,1,2,0,4,1,4,0,0,0,3,1,4,0,0,0,4
%N Largest number k > 0 such that n - k! is prime, or 0 if no such k exists.
%C If k > n, n - k! is negative and therefore, not prime.
%H Robert Israel, <a href="/A241424/b241424.txt">Table of n, a(n) for n = 1..10000</a>
%p a:= proc(n) local k, r;
%p r:= 0;
%p for k from 1 do
%p if k! >= n then return r
%p elif isprime(n-k!) then r:= k
%p fi
%p od
%p end proc:
%p seq(a(n),n=1..100); # _Robert Israel_, Aug 10 2014
%t a[n_] := Module[{k, r = 0}, For[k = 1, True, k++, If[k! >= n, Return[r], If[PrimeQ[n - k!], r = k]]]];
%t Array[a, 100] (* _Jean-François Alcover_, Jul 27 2020, after Maple *)
%o (PARI)
%o a(n)=forstep(k=n,1,-1,if(ispseudoprime(n-k!),return(k)))
%o n=1;while(n<150,print1(a(n),", ");n++)
%Y Cf. A175940, A245715.
%K nonn
%O 1,4
%A _Derek Orr_, Aug 08 2014