An Image from the Collatz Problem
By Andrew Shapira. The intensity of a point denotes the time taken to terminate.
Collatz 3n+1 Problem Structure
Observations posted by Ken Conrow to stimulate further research.
Collatz Problem
From Eric Weissten's World of Mathematics. Article with references and links.
Computational Verification of the 3x+1 Conjecture
Results up to 2^60 by Tomás Oliveira e Silva.
Experiments with the 3n+1 Sequence
An online calculator by Alfred Wassermann.
On The 3x + 1 Problem
These pages supply numerical data and propose some conjectures on this innocent looking problem. All numbers up to 29,300 * 10^12 ( ~ 26 * 2^50 ) have been checked for convergence.
The 3x + 1 Problem and its Generalizations
A survey article by Jeff Lagarias.
The 3x+1 Problem Annotated Bibliography
By Jeffrey Lagarias, 1997.
The 3x+1 Problem Conference Proceedings
Katholische Universität Eichstätt, Germany; 5--6 August 1999. On-line proceedings and group photo.
The Collatz 3n+1 Conjecture is Unprovable
A paper by Craig Alan Feinstein arguing that the Collatz Conjecture cannot be formally proved.
The Collatz Problem, Data and Models
Properties and predictive models for the Collatz Problem and relative functions.
The Generalised 3x+1 Problem
A survey by Keith Matthews [PDF].
The Structure of the 3x + 1 Function
Papers by Peter Schorer describing several new approaches.