<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>617</id>
    <completedYear>2020</completedYear>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>23</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>workingpaper</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation>Technische Hochschule Nürnberg</contributingCorporation>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2020-04-15</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Divisions by Two in Collatz Sequences</title>
    <abstract language="eng">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.</abstract>
    <identifier type="urn">urn:nbn:de:bvb:92-opus4-6172</identifier>
    <identifier type="doi">10.34646/thn/ohmdok-617</identifier>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Christian Koch</author>
    <author>Eldar Sultanow</author>
    <author>Sean Cox</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Collatz Conjecture</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Number Theory</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Data Science</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Collatz-Problem</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Zahlentheorie</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>swd</type>
      <value>Data Science</value>
    </subject>
    <collection role="ddc" number="5">Naturwissenschaften und Mathematik</collection>
    <thesisPublisher>Technische Hochschule Nürnberg Georg Simon Ohm</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-ohm/files/617/CollatzDivisionsByTwo.pdf</file>
  </doc>
</export-example>
