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Final nonzero digit of (n!)! (A000197).
2

%I #27 Dec 07 2023 11:40:22

%S 1,1,2,2,6,6,6,4,6,8,2,8,8,6,4,4,6,6,8,2,6,4,4,8,2,2,6,2,2,6,4,6,2,2,

%T 8,4,6,8,2,2,2,2,8,6,6,6,2,2,6,8,4,2,2,2,8,8,4,4,2,6,8,6,4,6,6,4,8,2,

%U 2,4,4,2,8,2,8,2,4,2,8,8,6,8,2,8,4,4,6,8,8,6,2,4,6,2,6,4,2,6,4,6,2,6,4,2,8,2,4,2

%N Final nonzero digit of (n!)! (A000197).

%H David W. Wilson, <a href="/A063944/b063944.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>

%o (PARI) for(n=0,22,m=n!!; while(Mod(m,10) == 0,m=m/10); print(Mod(m,10)))

%o (Python)

%o from functools import reduce

%o from math import prod, factorial

%o from sympy.ntheory.factor_ import digits

%o def A063944(n): return reduce(lambda x,y:x*y%10,((1,1,2,6,4)[a]*((6,2,4,8)[i*a&3] if i*a else 1) for i, a in enumerate(digits(factorial(n),5)[-1:0:-1])))*6%10 if n>1 else 1 # _Chai Wah Wu_, Dec 07 2023

%Y Cf. A000197, A008904.

%K nonn,base

%O 0,3

%A _Jason Earls_, Sep 01 2001

%E More terms from _David W. Wilson_, Sep 05 2001, who remarks that "I'll tell you, computing (107!)! took up some disk space!"