A generalization of the Collatz problem. Building cycles and a stochastic approach
type: Item
instance of: scholarly article
title: A generalization of the Collatz problem. Building cycles and a stochastic approach
zbMATH Open document ID: 1010.11016
DOI: 10.1023/A:1015122111180
published in: Journal of Statistical Physics
publication date: 2002-08-15T00:00:00Z
review text: The well-known and still unsolved \((3x+1)/2\)- or Collatz-problem is generalized into the \(n\)-furcation problem \((l_ix+m_i)/n\)-Problem. It is shown that, under some constraints on \(l_i\) and \(m_i\), the bijection property between the last \(k\) digits written in base \(n\) and the first \(k\) iterates is preserved. This is used to construct arbitrary cycles. Another goal of this paper is to complete the stochastic approach of the Collatz problem. It is conjectured, and tested on a large scale, that the behavior of the iterates started in a large interval around a large value (about \(10^9\)) is equivalent to the behavior obtained by selecting them randomly. In some sense the agreement is excellent.
reviewed by: Helmut Müller
Mathematics Subject Classification ID: 11B83
zbMATH DE Number: 1781680
zbMATH Keywords: 3x+1-problem
zbMATH Keywords: Collatz problem
author: J. L. Rouet
author: Marc R. Feix
MaRDI profile type: Publication
full work available at URL: a:1015122111180
OpenAlex ID: W1616967412
description: scientific article; zbMATH DE number 1781680