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A136692 Final nonzero digit of n! in base 5.

%I A136692 #14 Jun 27 2025 17:59:30
%S A136692 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,
%T A136692 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,
%U A136692 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
%N A136692 Final nonzero digit of n! in base 5.
%H A136692 Robert Israel, <a href="/A136692/b136692.txt">Table of n, a(n) for n = 0..10000</a>
%F A136692 a(n) = (n!/A243757(n)) mod 5. - _Ridouane Oudra_, Sep 27 2024
%e A136692 6! = 720 decimal = 10340 quinary, so a(6) = 4.
%p A136692 f:= proc(n) option remember;
%p A136692    local t;
%p A136692    t:= n / 5^padic:-ordp(n,5);
%p A136692    procname(n-1)*t mod 5
%p A136692 end proc:
%p A136692 f(0):= 1:
%p A136692 map(f, [$0..100]); # _Robert Israel_, Jun 27 2025
%t A136692 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 *)
%o A136692 (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
%Y A136692 Cf. A000142, A136690, A136691, A136693, A136694, A136695, A136696, A008904, A136697, A136698, A136699, A136700, A136701, A136702.
%Y A136692 Cf. A243757.
%K A136692 base,easy,nonn
%O A136692 0,3
%A A136692 _Carl R. White_, Jan 16 2008