Print the number of zeros for the years from 0 to 128 in the number systems from base 2 to base 128. Guess which Birthday has the most zeros!

mostRoundBirthday.py

import math

# Definition
class YearZeros:
    year = 0
    zeros = 0
    base = set() # Store the year inf form of 'all' (2 to 128) bases here. E.g. year 4 would be 

# Declaration
result = []

# Number characters
characters = [u"0",u"1",u"2",u"3",u"4",u"5",u"6",u"7",u"8",u"9",u"a",u"b",u"c",u"d",u"e",u"f",u"g",u"h",u"i",u"j",u"k",u"l",u"m",u"n",u"o",u"p",u"q",u"r",u"s",u"t",u"u",u"v",u"w",u"x",u"y",u"z",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600",u"\U0001F600"]

def getNumber(decimalNumber, base, characters):
    remainder = -1
    denominator = decimalNumber
    goOn = True
    result = u""
    
    while goOn:
        remainder = denominator % base
        denominator = int(math.floor(denominator / base))
        result = characters[remainder] + result
        if denominator == 0:
            goOn = False
    #print u"From: " + str(decimalNumber).encode('utf-8') + u"  to: " + str(result).encode('utf-8')
    return result

#getNumber(5, 2, characters)
#getNumber(20, 10, characters)
#getNumber(20, 16, characters)
#getNumber(40, 56, characters)

# Initialize
for year in range(0, 129):
    #print year
    result.append(YearZeros())
    result[year].year = year
    result[year].base = []

# Represent the year in all bases and store it in the base array as a string.
for base in range (2, 129):
    for year in range (0, 129):
        result[year].base.append(getNumber(year, base, characters))
        
# Sum zeros
for year in range(0, 129):
    for base in range (0, 127):
        for char in result[year].base[base]:
            if char == u"0":
                result[year].zeros += 1

# Print results
print "year;zeros;numbers"
for year in range(0, 129):
    print str(year) + ";" + str(result[year].zeros) + ";" + str(result[year].base)