A solution to SMBC #2874. http://www.smbc-comics.com/index.php?db=comics&id=2874#comic

fouriest.py

import string
# Algorithm for SMBC #2874 - the "fouriest" transform.
# Support bases 2-36.
BASE_LIST = string.digits + string.letters


def encode(integer, base):
    # Stolen off the internet from somewhere,
    # almost certainly guaranteed to be buggy.
    base_list = BASE_LIST[:base]
    ret = ''
    while integer != 0:
        ret = base_list[integer % base] + ret
        integer /= base
    return ret

def transform(inp):
    # inp (integer) - A base-10 encoded integer to be transformed.
    # Returns (best_string, best_base) tuple.
    inp_str = str(inp)
    best_base = '10'
    best_string = inp_str
    max_num_fours = inp_str.count('4')
    for i in range(5, len(BASE_LIST)):
        # No base less than 5 will contain any '4' characters.
        tmp = encode(inp, i)
        cnt = tmp.count('4')
        if cnt > max_num_fours:
            max_num_fours = cnt
            best_base = str(i)
            best_string = tmp
    return best_string, best_base


# Usage:
# fouriest.transform(624)
# ('4444', '5')