Number Theory

    

Bit-Position Dynamics and a Lower Bound for Collatz Cycle Length

Authors: Jochen Kiemes

We present a novel reformulation of the Collatz conjecture by leveraging the binary structure of positive integers, focusing on the sequence of odd terms. Through an analysis of leading and trailing bit-position dynamics, we derive a substantial lower bound of at least 17,026,679,261 steps for any hypothetical non-trivial cycle, offering new insights into its structural constraints.

Comments: 7 Pages.

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Submission history

[v1] 2025-04-21 20:54:23

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