A182577 Number of ones in Zeckendorf representation of n!

1, 1, 1, 2, 2, 4, 3, 5, 6, 9, 8, 11, 11, 11, 16, 17, 17, 18, 23, 23, 28, 31, 33, 27, 33, 29, 40, 37, 42, 42, 41, 44, 47, 44, 53, 56, 57, 50, 64, 55, 59, 68, 63, 72, 70, 61, 69, 85, 80, 83, 87, 97, 98, 101, 87, 91, 100, 102, 114, 108, 116, 109, 117, 117, 113, 124

Offset: 0

Author

Alex Ratushnyak, May 05 2012

Keywords

• nonn

Examples

			5! = {1, 0, 0, 1, 0, 1, 0, 0, 1, 0} in the Zeckendorf base.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007895, A020908, A020910, A025496-A025502, A182535, A182576, A000142.

Programs

Python

from math import factorial
def A182577(n):
    m, tlist, s = factorial(n), [1,2], 0
    while tlist[-1]+tlist[-2] <= m:
        tlist.append(tlist[-1]+tlist[-2])
    for d in tlist[::-1]:
        if d <= m:
            s += 1
            m -= d
    return s # Chai Wah Wu, Jun 15 2018