A136701 Final nonzero digit of n! in base 15.

1, 1, 2, 6, 9, 8, 3, 6, 3, 12, 3, 3, 6, 3, 12, 12, 12, 9, 12, 3, 9, 9, 3, 9, 6, 9, 9, 3, 9, 6, 12, 12, 9, 12, 3, 12, 12, 9, 12, 3, 3, 3, 6, 3, 12, 6, 6, 12, 6, 9, 12, 12, 9, 12, 3, 6, 6, 12, 6, 9, 6, 6, 12, 6, 9, 9, 9, 3, 9, 6, 3, 3, 6, 3, 12, 9, 9, 3, 9, 6, 12, 12, 9, 12, 3, 12, 12, 9, 12, 3, 3, 3, 6

Offset: 0

Author

Carl R. White, Jan 16 2008

Keywords

• base
• easy
• nonn

Comments

From Robert Israel, Jun 08 2018: (Start)

For n >= 6, a(n) is 3, 6, 9 or 12.

For k >= 2, a(5*k) = a(5*k+1) = a(5*k+3). (End)

Examples

			6! = 720 decimal = 330 quindecimal, so a(6) = 3.
		

Links

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

Crossrefs

Cf. A000142, A136690, A136691, A136692, A136693, A136694, A136695, A136696, A008904, A136697, A136698, A136699, A136700, A136702.

Programs

Maple

a:= 1: b:= 0: R[0]:= 1:
for n from 1 to 100 do
   alpha:= padic:-ordp(n,3);
   beta:= padic:-ordp(n,5);
   a:= a * n/3^alpha/5^beta;
   b:= b + alpha - beta;
   R[n]:= a * 3 &^ b mod 15;
od:
seq(R[n],n=0..100); # Robert Israel, Jun 08 2018

Mathematica

nzd[x_]:=If[x[[-1,1]]==0,x[[-2,1]],x[[-1,1]]]; Table[nzd[Split[IntegerDigits[n!,15]]],{n,0,100}] (* Harvey P. Dale, Jul 11 2023 *)