this weekend's python class assignment

[scidam]

This problem interested me, and I solved its more general version: when one asked to find decomposition by powers not only of 2, but
arbitrary number.

from itertools import accumulate
def decompose(a, base=2):
    """Decompose the number by powers of specified base. 
    
    4672 = 2**12 + 2**9 + 2**6 (base = 2)
    """
    res = list()
    def _recursion(a, res=res):
        if a % base != 0:
            raise Exception("Couldn't decompose the number.")
        ind = 0
        while a % base == 0:
            a = a / base 
            ind += 1
        if ind:
            res.append(ind)
        if a == 1:
            return list(accumulate(res))
        if a > 1:
            a -= 1
            _recursion(a, res=res)
    _recursion(a)
    return list(accumulate(res))

decompose(4672)

Output:
[6, 9, 12]

decompose(4672, base=4)

Output:
[3, 4, 4, 6]  # 4672 = 4**3 + 4**4 + 4**4 + 6**4

decompose(4672, base=8)

Output:
[2, 3, 4]  # 4372 = 8**2 + 8**3 + 8**4

Finally,

decompose(173688133855974293135356477513031861779904976998460846059186376011869694459904, base=2)

Output:
[255, 256]

decompose(173688133855974293135356477513031861779904976998460846059186376011869694459904, base=8)

Output:
[85, 85, 85] # big number = 8**85 + 8**85 + 8**85