The 3x+1 problem: An annotated bibliography (1963--1999) (sorted by author)

TL;DR

This paper provides a comprehensive annotated bibliography of research on the 3x+1 problem from 1963 to 1999, summarizing the progress and challenges in understanding this longstanding unsolved conjecture.

Contribution

It compiles and annotates historical research on the 3x+1 problem, highlighting key developments and unresolved questions over several decades.

Findings

The 3x+1 Conjecture remains unproven.

Numerous partial results and computational verifications exist.

The problem continues to attract mathematical interest.

Abstract

The 3x+ 1 problem concerns iteration of the map on the integers given by T(n) = (3n+1)/2 if n is odd; T(n) = n/2 if n is even. The 3x+1 Conjecture asserts that for every positive integer n > 1 the forward orbit of n under iteration by T includes the integer 1. This paper is an annotated bibliography of work done on the 3x+1 problem and related problems from 1963 through 1999. At present the 3x+1 Conjecture remains unsolved.