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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()