On the nonexistence of cycles for the Collatz function

2012/08/13 by Manfred Bork, Bork, Manfred
Computer Science · Mathematics · #11B83 #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #Digital Media Forensic Detection #FOS: Mathematics #General Mathematics (math.GM)

paper · pdf · doi:10.48550/arxiv.1208.2556

openalex publication_date 2012/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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