What question did this study set out to answer?

This research aims to explore how the block length affects convergence in a Collatz-type map with alternating odd-step rules.

April 19, 2026Open Access

Collatz-Type Maps with Alternating 3n±1

Key Points

This research aims to explore how the block length affects convergence in a Collatz-type map with alternating odd-step rules.
Investigated a Collatz-type map with odd steps defined as alternating between 3n + 1 and 3n - 1.
Performed computations up to 10 million to analyze convergence patterns.
Examined the behavior particularly at block length L = 2.
At block length L = 2, around half of the initial values enter a unique 44-cycle.
Convergence behavior shows significant variation based on the block length used.

Abstract

We study a Collatz-type map in which the odd-step alternates between 3n + 1 and 3n − 1. Computations up to 107 show that convergence depends strongly on the block length L, with a singular behavior at L = 2, where approximately half of the initial values enter a unique 44-cycle.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Masanori Fujii (Fri,) studied this question.

synapsesocial.com/papers/69e47376010ef96374d8f349 https://doi.org/https://doi.org/10.5281/zenodo.19632916

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Bookmark

View Full Paper