A Cubic Upper Bound Conjecture for Odd Collatz Trajectories

This preprint introduces a conjectural cubic upper bound for odd trajectories of the Collatz map. For an odd positive starting integer, the conjecture concerns the maximum odd value attained along its accelerated odd-only Collatz trajectory.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-20
DOI
https://doi.org/10.5281/zenodo.22849199
Primary Topic
Benford’s Law and Fraud Detection
Type
preprint
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preprint

A Cubic Upper Bound Conjecture for Odd Collatz Trajectories

Chandra Shekhar Shivam
Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
preprint

A Cubic Upper Bound Conjecture for Odd Collatz Trajectories

Chandra Shekhar Shivam
preprint en

Abstract

This preprint introduces a conjectural cubic upper bound for odd trajectories of the Collatz map. For an odd positive starting integer, the conjecture concerns the maximum odd value attained along its accelerated odd-only Collatz trajectory.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Benford’s Law and Fraud Detection
DOIOpen Access PDFOpenAlex
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A Cubic Upper Bound Conjecture for Odd Collatz Trajectories — Chandra Shekhar Shivam · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS