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

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, 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, 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

Offset: 1

Author

Derek Orr, Aug 08 2014

Keywords

• nonn

Comments

If k > n, n - k! is negative and therefore, not prime.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A175940, A245715.

Programs

Maple

a:= proc(n) local k, r;
r:= 0;
for k from 1 do
   if k! >= n then return r
   elif isprime(n-k!) then r:= k
   fi
od
end proc:
seq(a(n),n=1..100); # Robert Israel, Aug 10 2014

Mathematica

a[n_] := Module[{k, r = 0}, For[k = 1, True, k++, If[k! >= n, Return[r], If[PrimeQ[n - k!], r = k]]]];
Array[a, 100] (* Jean-François Alcover, Jul 27 2020, after Maple *)

PARI

a(n)=forstep(k=n,1,-1,if(ispseudoprime(n-k!),return(k)))
n=1;while(n<150,print1(a(n),", ");n++)