Find counter examples to the conjecture: The orbit of all strictly positive natural numbers through col3 ends up in one of the two finite cycles.

col3.py

#!/usr/bin/env python3
"""
Find counter examples to the conjecture:
The orbit of all strictly positive natural numbers
through col3 ends up in either C[0] and C[1].
"""
# Ignores PEP8 and pylint for brevity and math-friendly notation.

import sys

C = [
        {1, 6, 2, 9, 3},
        # trivial cycle
        {21, 7, 30, 10, 42, 14, 57, 19, 78, 26, 105, 35, 141, 47, 189, 63}
        # the "other" cycle
]

def col3(n):
    """Collatz-like function based on % 3"""
    m = n % 3
    if m == 0:
        return n / 3
    if m == 1:
        return 4 * n + 2
    if m == 2:
        return 4 * n + 1

def cycle(n):
    """Find the cycle in which n ends up"""
    start = n
    while True:
        for i in range(0, 2):
            if start in C[i]:
                return i
            start = col3(start)

def main():
    if len(sys.argv) < 2:
        return
    counter_examples = []
    for n in range(1, int(sys.argv[1])):
        if cycle(n) > 1:
            counter_examples.append(n)
    print(counter_examples)  # []

if __name__ == "__main__":
    main()