A008906 Number of digits in n! excluding final zeros.

1, 1, 1, 1, 2, 2, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 15, 16, 18, 19, 20, 20, 21, 23, 24, 25, 26, 27, 29, 30, 32, 33, 34, 36, 37, 39, 39, 41, 43, 44, 46, 47, 48, 50, 52, 53, 53, 55, 56, 58, 60, 61, 62, 64, 66, 68, 68, 70, 72, 74, 76, 76, 78, 80, 82, 84, 85, 86, 88, 90, 92, 92, 94

Offset: 0

Author

Russ Cox

Keywords

• nonn
• base
• easy

Comments

From Bernard Schott, Nov 19 2021: (Start)

a(n) < n iff 2 <= n <= 38 or n = 40;

a(n) = n iff n = 1, 39, 41;

a(n) > n iff n = 0 or n >= 42. (End)

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to final digits of numbers

Crossrefs

Cf. A027868, A034886.

Programs

Mathematica

Array[IntegerLength[#!//.x_/;x~Mod~10==0:>x/10]&,77,0] (* Giorgos Kalogeropoulos, Nov 19 2021 *)

Python

from math import factorial
def A008906(n): return len(str(factorial(n)).rstrip('0')) # Chai Wah Wu, Oct 24 2021

Formula

a(n) = A034886(n) - A027868(n). - Michel Marcus, Jun 24 2013