A136692 Final nonzero digit of n! in base 5.

1, 1, 2, 1, 4, 4, 4, 3, 4, 1, 2, 2, 4, 2, 3, 4, 4, 3, 4, 1, 4, 4, 3, 4, 1, 1, 1, 2, 1, 4, 4, 4, 3, 4, 1, 2, 2, 4, 2, 3, 4, 4, 3, 4, 1, 4, 4, 3, 4, 1, 2, 2, 4, 2, 3, 3, 3, 1, 3, 2, 4, 4, 3, 4, 1, 3, 3, 1, 3, 2, 3, 3, 1, 3, 2, 1, 1, 2, 1, 4, 4, 4, 3, 4, 1, 2, 2, 4, 2, 3, 4, 4, 3, 4, 1, 4, 4, 3, 4, 1

Offset: 0

Author

Carl R. White, Jan 16 2008

Keywords

• base
• easy
• nonn

Examples

			6! = 720 decimal = 10340 quinary, so a(6) = 4.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000142, A136690, A136691, A136693, A136694, A136695, A136696, A008904, A136697, A136698, A136699, A136700, A136701, A136702.

Cf. A243757.

Programs

Maple

f:= proc(n) option remember;
   local t;
   t:= n / 5^padic:-ordp(n,5);
   procname(n-1)*t mod 5
end proc:
f(0):= 1:
map(f, [$0..100]); # Robert Israel, Jun 27 2025

Mathematica

Table[Module[{sp=Split[IntegerDigits[n!,5]]},If[sp[[-1,-1]]==0,sp[[-2, -1]], sp[[-1,-1]]]],{n,0,100}] (* Harvey P. Dale, Oct 26 2016 *)

PARI

a(n)={my(v=[1, 1, 2, 1, 4, 4, 4, 3, 4, 1]); if(n==0, 1, lift(prod(k=0, logint(n,5), Mod(v[1 + n\5^k % 10], 5))))} \\ Andrew Howroyd, Sep 27 2024

Formula

a(n) = (n!/A243757(n)) mod 5. - Ridouane Oudra, Sep 27 2024