```
from __future__ import annotations
def collatz_sequence(n: int) -> list[int]:
"""
Collatz conjecture: start with any positive integer n. The next term is
obtained as follows:
If n term is even, the next term is: n / 2 .
If n is odd, the next term is: 3 * n + 1.
The conjecture states the sequence will always reach 1 for any starting value n.
Example:
>>> collatz_sequence(2.1)
Traceback (most recent call last):
...
Exception: Sequence only defined for natural numbers
>>> collatz_sequence(0)
Traceback (most recent call last):
...
Exception: Sequence only defined for natural numbers
>>> collatz_sequence(43) # doctest: +NORMALIZE_WHITESPACE
[43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7,
22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1]
"""
if not isinstance(n, int) or n < 1:
raise Exception("Sequence only defined for natural numbers")
sequence = [n]
while n != 1:
n = 3 * n + 1 if n & 1 else n // 2
sequence.append(n)
return sequence
def main():
n = 43
sequence = collatz_sequence(n)
print(sequence)
print(f"collatz sequence from {n} took {len(sequence)} steps.")
if __name__ == "__main__":
main()
```