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Divisions by Two in Collatz Sequences: A Data Science Approach (2nd ed.)

  • 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 develop and prove an equation to calculate the maximum possible number of divisions by two for any given a Collatz sequence. Whenever this maximum is reached, a sequence leads to the result one, as conjectured by Lothar Collatz. Furthermore, we show how many divisions by two are required for a cycle of a specific length. The findings are valuable 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-opus4-6208
DOI:https://doi.org/10.34646/thn/ohmdok-620
Subtitle (English):Working Paper Technische Hochschule Nürnberg 05 May 2020
Document Type:Working Paper
Language:English
Publishing Institution:Technische Hochschule Nürnberg Georg Simon Ohm
Creating Corporation:Technische Hochschule Nürnberg
Release Date:2020/05/07
Tag:Collatz Conjecture; Data Science; Divisions by Two
GND Keyword:Collatz-Problem; Zahlentheorie; Data Science
Edition:2nd ed.
Pagenumber:25
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik
Licence (German):Creative Commons - CC BY - Namensnennung 4.0 International
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