%I #7 Aug 01 2015 13:53:40

%S 1,1,2,6,11,3,5,9,7,11,6,1,12,12,12,11,7,2,10,8,4,6,2,7,12,1,2,2,4,12,

%T 9,6,10,5,1,9,12,2,11,7,7,1,3,12,8,9,11,10,12,3,7,6,11,11,9,1,4,7,3,8,

%U 12,4,1,11,2,10,10,7,8,6,4,11,12,5,6,8,10,3,5,5,10,4,3,2,12,6,9,3,4,5,8,4

%N Final nonzero digit of n! in base 13.

%e 6! = 720 decimal = 435 tridecimal, so a(6) = 5.

%t f[s_List] := Block[{a = s[[ -1]], len = Length@s}, Append[s, If[Mod[len, 13] == 0, Mod[a*len/13,13], Mod[a*len, 13]]]]; Nest[f, {1}, 100] (* _Robert G. Wilson v_, May 03 2009 *)

%t f[n_] := Block[{id = IntegerDigits[n!, 13]}, While[id[[ -1]] == 0, id = Most@id]; id[[ -1]]]; Table[ f@n, {n, 0, 100}] (* _Robert G. Wilson v_, May 03 2009 *)

%Y Cf. A000142, A136690, A136691, A136692, A136693, A136694, A136695, A136696, A008904, A136697, A136698, A136700, A136701, A136702.

%K base,easy,nonn

%O 0,3

%A _Carl R. White_, Jan 16 2008