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

0,4

Links

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A159268 A058723 A329436 * A357189 A241450 A189675

Adjacent sequences: A182574 A182575 A182576 * A182578 A182579 A182580

Keyword

nonn

Author

Alex Ratushnyak, May 05 2012

Status

approved