#!/usr/bin/env python
"""
This Python script searches for powers whose decimal expansions do not 
contain any zero digits. It accepts up to four optional arguments.

Arguments:

    base:     the base of exponents (default is 5)
    max_iter: largest exponent to check (default is 10**6)
    digits:   initial number of digits to check (default is 60)
    start:    first exponent to check (default is 0)

Output:

    The program prints the exponents n for which the decimal expansion 
    of base**n does not contain any zero digits. One number is printed
    on each line.

    If the program is interrupted by pressing Ctrl-C, then the current
    value of the exponent n will be displayed, allowing you to restart
    the search where you left off.

Caveat:
    It is extremely unlikely that a power with millions of digits
    will have no zero digits. However, if this should occur, then
    the program may crash.
"""

import sys
import signal
from math import log10


def has_zero_digit(n):
    return '0' in str(n)


def verify(n, base, power, digits, max_power):
    if not has_zero_digit(power):
        log = n * log10(base)
        while digits <= log:
            digits *= 2
            max_power *= max_power
            power = pow(base, n, max_power)
            if has_zero_digit(power):
                return
        print (n)
        

def search(base, max_iter, digits, start):
    global n
    max_power = 10 ** digits
    n = start

    if start * log10(base) < digits:
        power = base ** start
        while power < max_power:
            if not has_zero_digit(power):
                print (n)
            power *= base
    	    n += 1
        power = power % max_power
    else:
        power = pow(base, start, max_power)

    while n <= max_iter:
        verify(n, base, power, digits, max_power)
        power = (power * base) % max_power
        n += 1



def exit_gracefully(signum, frame):
    print ('Interrupted at n = %d' % n)
    sys.exit(1)
        

if __name__ == '__main__':
    base = 5
    max_iter = 10**6
    digits = 60
    start = 0
    n = 0
    num_args = len(sys.argv)
    if num_args > 1:
        base = int(sys.argv[1])
    if num_args > 2:
        max_iter = int(sys.argv[2])
    if num_args > 3:
        digits = int(sys.argv[3])
    if num_args > 4:
        start = int(sys.argv[4])

    signal.signal(signal.SIGINT, exit_gracefully)
    search(base, max_iter, digits, start)