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

0,3

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)

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A242433 A011046 A246828 * A374695 A175030 A335027

Adjacent sequences: A136698 A136699 A136700 * A136702 A136703 A136704

Keyword

base,easy,nonn

Author

Carl R. White, Jan 16 2008

Status

approved