A063944 Final nonzero digit of (n!)! (A000197).

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, 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, 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

Offset: 0

Author

Jason Earls, Sep 01 2001

Keywords

• nonn
• base

Links

• David W. Wilson, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to final digits of numbers

Crossrefs

Cf. A000197, A008904.

Programs

PARI

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

Python

from functools import reduce
from math import prod, factorial
from sympy.ntheory.factor_ import digits
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

Extensions

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