A072831 Number of bits in n!.

1, 1, 2, 3, 5, 7, 10, 13, 16, 19, 22, 26, 29, 33, 37, 41, 45, 49, 53, 57, 62, 66, 70, 75, 80, 84, 89, 94, 98, 103, 108, 113, 118, 123, 128, 133, 139, 144, 149, 154, 160, 165, 170, 176, 181, 187, 192, 198, 203, 209, 215, 220, 226, 232, 238, 243, 249, 255, 261, 267

Offset: 0

Author

Rick L. Shepherd, Jul 22 2002

Keywords

• base
• nonn

Examples

			a(4)=5 because 4! = 4*3*2*1 = 24 (base 10) = 11000 (base 2), using 5 bits.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A034886 (decimal digits of n!), A000142 (n!). Essentially the same as A003070.

Programs

Maple

a:= n-> 1+ilog2(n!):
seq(a(n), n=0..100);  # Alois P. Heinz, May 03 2016

Mathematica

Floor[Log[2,Range[0,60]!]]+1 (* Harvey P. Dale, Nov 16 2011 *)

PARI

for(n=0,100,print1(floor(log(n!)/log(2))+1,","))

PARI

a(n) = #binary(n!); \\ Michel Marcus, Dec 23 2016

Python

import math
def a(n):
  return len(bin(math.factorial(n))[2:]) # Indranil Ghosh, Dec 23 2016

Formula

a(n) = floor(log(n!)/log(2)) + 1.