A078565 Number of zeros in the binary expansion of n!.

0, 0, 1, 1, 3, 3, 6, 7, 10, 13, 11, 19, 17, 21, 25, 23, 27, 27, 30, 40, 40, 41, 42, 44, 51, 54, 54, 56, 56, 63, 60, 71, 76, 77, 77, 77, 88, 86, 90, 90, 97, 99, 106, 105, 107, 117, 115, 117, 114, 122, 126, 130, 138, 138, 151, 144, 146, 157, 160, 158, 160, 176

Offset

0,5

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Formula

a(n) = A072831(n) - A079584(n). - Michel Marcus, Dec 23 2016

Example

a(4) = 3 because 4! = 24_10 = 11000_2 and it has 3 zero digits.

Mathematica

Table[Count[IntegerDigits[n!, 2], 0], {n, 0, 100}] (* T. D. Noe, Apr 10 2012 *)
DigitCount[Range[0, 70]!, 2, 0] (* Harvey P. Dale, Mar 11 2019 *)

Prog

(PARI) for(n=1, 300, b=binary(n!); print1(sum(k=1, length(b), if(b[k], 0, 1))", "))
(Python)
import math
def a(n):
    return bin(math.factorial(n))[2:].count("0")
# Indranil Ghosh, Dec 23 2016

Crossrefs

Cf. A072831, A079584.

Sequence in context: A333885 A270060 A350636 * A211541 A026926 A332557

Adjacent sequences: A078562 A078563 A078564 * A078566 A078567 A078568

Keyword

nonn,base

Author

Jose R. Brox (tautocrona(AT)terra.es), Jan 26 2003

Status

approved