threezeros.1.py

def BaseSeven(num):
    powersOfSeven = 1;
    res = 0;
    while num / powersOfSeven > 6: powersOfSeven = powersOfSeven * 7
    while powersOfSeven != 1:
        res = res * 10 + int(num / powersOfSeven)
        num = num - int(num / powersOfSeven) * powersOfSeven
        powersOfSeven = powersOfSeven / 7
    res = res * 10 + num
    return res

def HasThreeZeros(num):
    return str(num).find("000") != -1

def FindWithoutZeros(power):
    lastWithoutThreeZeros = power
    failures = -1
    num = pow(2, power)
    while failures <= lastWithoutThreeZeros:
        if HasThreeZeros(BaseSeven(num)):
           failures = failures + 1
        else:
            failures = 0
            lastWithoutThreeZeros = power
            print power
        power = power + 1
        num = num * 2
        if (float(power) / 100) == int(power / 100): print "CheckPoint:", power
    return lastWithoutThreeZeros

print FindWithoutZeros(1)