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.
Author: | Christian KochORCiD, Eldar Sultanow, Sean Cox |
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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 |