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A136701 Final nonzero digit of n! in base 15.

%I A136701 #10 Jul 11 2023 14:56:02
%S A136701 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,
%T A136701 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,
%U A136701 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
%N A136701 Final nonzero digit of n! in base 15.
%C A136701 From _Robert Israel_, Jun 08 2018: (Start)
%C A136701 For n >= 6, a(n) is 3, 6, 9 or 12.
%C A136701 For k >= 2, a(5*k) = a(5*k+1) = a(5*k+3). (End)
%H A136701 Robert Israel, <a href="/A136701/b136701.txt">Table of n, a(n) for n = 0..10000</a>
%e A136701 6! = 720 decimal = 330 quindecimal, so a(6) = 3.
%p A136701 a:= 1: b:= 0: R[0]:= 1:
%p A136701 for n from 1 to 100 do
%p A136701    alpha:= padic:-ordp(n,3);
%p A136701    beta:= padic:-ordp(n,5);
%p A136701    a:= a * n/3^alpha/5^beta;
%p A136701    b:= b + alpha - beta;
%p A136701    R[n]:= a * 3 &^ b mod 15;
%p A136701 od:
%p A136701 seq(R[n],n=0..100); # _Robert Israel_, Jun 08 2018
%t A136701 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 *)
%Y A136701 Cf. A000142, A136690, A136691, A136692, A136693, A136694, A136695, A136696, A008904, A136697, A136698, A136699, A136700, A136702.
%K A136701 base,easy,nonn
%O A136701 0,3
%A A136701 _Carl R. White_, Jan 16 2008