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

0,5

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A027868, A034886.

Sequence in context: A029096 A194820 A076872 * A029074 A258741 A036016

Adjacent sequences: A008903 A008904 A008905 * A008907 A008908 A008909

Keyword

nonn,base,easy

Author

Russ Cox

Status

approved