The 3x+1 Problem: An Annotated Bibliography, II (2000-2009)

TL;DR

This paper provides a comprehensive annotated bibliography of research on the 3x+1 problem from 2000 to 2009, summarizing progress and open questions in understanding the conjecture's behavior.

Contribution

It compiles and analyzes research from 2000-2009 on the 3x+1 problem, highlighting developments and unresolved issues in the conjecture.

Findings

Extensive research compiled and summarized

The 3x+1 Conjecture remains unsolved

Identifies key directions for future work

Abstract

The 3x+1 problem concerns iteration of the map T(n) =(3n+1)/2 if n odd; n/2 if n even. The 3x +1 Conjecture asserts that for every positive integer n>1 the forward orbit of n includes the integer 1. This paper is an annotated bibliography of work done on the 3x+1 problem published from 2000 through 2009, plus some later papers that were preprints by 2009. This is a sequel to an annotated bibliography on the 3x+1 problem covering 1963-1999. At present the 3x+1 Conjecture remains unsolved.