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arXiv · 1208.2556

On the nonexistence of cycles for the Collatz function

Manfred Bork
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Abstract

The Collatz function is defined as C(n) = n / 2 if n is even and C(n) = 3n + 1 if n is odd. The Collatz conjecture states that every sequence generated by the Collatz function ends with the cycle (4, 2, 1) after a finite number of iterations. In this paper it is shown that there exists no other cycle for the Collatz function.

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Manfred Bork. 2012-08-13. On the nonexistence of cycles for the Collatz function. https://arxiv.org/abs/1208.2556

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