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Final nonzero digit of n! in base 5.
14

%I #10 Sep 28 2024 13:00:15

%S 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 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 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 Final nonzero digit of n! in base 5.

%F a(n) = (n!/A243757(n)) mod 5. - _Ridouane Oudra_, Sep 27 2024

%e 6! = 720 decimal = 10340 quinary, so a(6) = 4.

%t 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 (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 Cf. A000142, A136690, A136691, A136693, A136694, A136695, A136696, A008904, A136697, A136698, A136699, A136700, A136701, A136702.

%Y Cf. A243757.

%K base,easy,nonn

%O 0,3

%A _Carl R. White_, Jan 16 2008