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A241424 Largest number k > 0 such that n - k! is prime, or 0 if no such k exists.

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