The \(3x+1\) problem as a string rewriting system
type: Item
instance of: scholarly article
title: The \(3x+1\) problem as a string rewriting system
zbMATH Open document ID: 1229.11022
DOI: 10.1155/2010/458563
author: Joseph Sinyor
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2011-02-08T00:00:00Z
review text: Let \(T^k(n)\) be the value after \(k\) iterations in the \(3x+1\) problem. The author reformulates the conjecture in two assertions: (I) Every odd \(n\) lies on a distinct \(3x+1\) trajectory between two Mersenne numbers \(2^k-1\) or their equivalents; (II) If \(T^r(2^k-1)\to 2^l-1\) for any \(r,k,l>0\) then \(l<k\).
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 68Q42
zbMATH DE Number: 5847817
zbMATH Keywords: \(3x+1\) problem
Wikidata QID: Q58651769
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2010/458563
OpenAlex ID: W2028841589
cites work: Maximum excursion and stopping time record-holders for the problem: Computational results
cites work: The 3x + 1 Problem and Its Generalizations
cites work: The dynamical system generated by the \(3n+1\) function
cites work: Q4005194
cites work: Q3338316
cites work: On the \(3x+1\) problem
cites work: On the Collatz 3n + 1 Algorithm
cites work: Q4002287
DBLP publication ID: journals/ijmmsc/Sinyor10
description: scientific article; zbMATH DE number 5847817