Divisions by Two in Collatz Sequences

  • The Collatz conjecture is an unsolved number theory problem. We approach the question by examining the divisions by two that are performed within Collatz sequences. Aside from classical mathematical methods, we use techniques of data science. Based on the analysis of 10,000 sequences we show that the number of divisions by two lies within clear boundaries. Building on the results, we formulate and prove several theorems on the occurrence of cycles and the termination of Collatz sequences. The findings are useful for further investigations and could form the basis for a comprehensive proof of the conjecture.

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Metadaten
Author:Christian KochORCiD, Eldar Sultanow, Sean Cox
URN:urn:nbn:de:bvb:92-opus4-6172
DOI:https://doi.org/10.34646/thn/ohmdok-617
Document Type:Working Paper
Language:English
Publishing Institution:Technische Hochschule Nürnberg Georg Simon Ohm
Contributing Corporation:Technische Hochschule Nürnberg
Release Date:2020/04/17
Tag:Collatz Conjecture; Data Science; Number Theory
GND Keyword:Collatz-Problem; Zahlentheorie; Data Science
Pagenumber:23
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik
Licence (German):Creative Commons - CC BY - Namensnennung 4.0 International
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