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URL: https://oeis.org/A136692

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A136692
Final nonzero digit of n! in base 5.
15
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, 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, 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
OFFSET
0,3
LINKS
FORMULA
a(n) = (n!/A243757(n)) mod 5. - Ridouane Oudra, Sep 27 2024
EXAMPLE
6! = 720 decimal = 10340 quinary, so a(6) = 4.
MAPLE
f:= proc(n) option remember;
local t;
t:= n / 5^padic:-ordp(n, 5);
procname(n-1)*t mod 5
end proc:
f(0):= 1:
map(f, [$0..100]); # Robert Israel, Jun 27 2025
MATHEMATICA
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 *)
PROG
(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
KEYWORD
base,easy,nonn
AUTHOR
Carl R. White, Jan 16 2008
STATUS
approved