Bases in which some 2^x doesn't contain a digit that is 2^x

digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZαβγδεζηθικλμνξοπρστυφχψω"

# Search for bases up to b
def powers(b):
    # Bases where some number passed
    bases = []

    for base in range(2,b+1):
        # Did any number in base pass the test?
        pass_in_base = False

        for i in range(1025):
            # Get p as a list of powers in base
            p = convert_base(2**i, base)
            powers_of_2 = []

            # Get all one-digit powers of 2 up
            j = 0
            while 2**j < base:
                powers_of_2.append(2**j)
                j += 1

            # Check whether p cointains a power of 2
            p_passes = True
            for power in powers_of_2:
                if power in p:
                    p_passes = False

            if p_passes:
                # Remove comment and break to show which numbers passed
                '''p_str = ""
                for j in p:
                    p_str += digits[j]
                print("In base", base, "the following number passes", p_str)'''
                pass_in_base = True
                break

        if pass_in_base:
            bases.append(base)
    print(bases)


def convert_base(n, b):
    if n == 0:
        return [0]
    digits = []
    while n:
        digits.append(int(n % b))
        n //= b
    return digits[::-1]