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A072831 Number of bits in n!. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

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

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

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

Sequence in context: A096221 A258084 A120367 * A072388 A101433 A225645

Adjacent sequences:  A072828 A072829 A072830 * A072832 A072833 A072834

KEYWORD

base,nonn

AUTHOR

Rick L. Shepherd, Jul 22 2002

STATUS

approved

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Last modified September 22 12:42 EDT 2019. Contains 327307 sequences. (Running on oeis4.)