How many numbers satisfy the \(3x+1\) conjecture?
type: Item
instance of: scholarly article
title: How many numbers satisfy the \(3x+1\) conjecture?
zbMATH Open document ID: 0685.10008
DOI: 10.1155/S0161171289000979
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46421
review text: Summary: Let \(\theta(x)\) be the number of numbers not exceeding \(x\) satisfy the \(3x+1\)-conjecture. We obtain a system of difference inequalities on functions closely related to \(\theta\). Solving this system in the simplest case, we establish \(\theta(x)>cx^{3/7}\). This improves a result of \textit{R. E. Crandall} [Math. Comput. 32, 1281--1292 (1978; Zbl 0395.10013)].
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 4122053
zbMATH Keywords: Collatz problem
zbMATH Keywords: \(3x+1\) conjecture
zbMATH Keywords: system of difference inequalities
Wikidata QID: Q122952185
author: Ilia Krasikov
MaRDI profile type: Publication
OpenAlex ID: W1572082656
description: scientific article; zbMATH DE number 4122053