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The 3x + 1 Problem and its Generalizations
- An activated-text 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.
Collatz 3n+1 Problem Structure
- Observations posted by Ken Conrow to stimulate further research.
- From Eric Weissten's World of Mathematics. Article with references and links.
The Collatz Problem, data and models
- Properties and predictive models for the Collatz Problem and related functions.
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.
The Generalised 3x+1 Problem
- A survey by Keith Matthews.
An Image from the Collatz Problem
- By Andrew Shapira. The intensity of a point denotes the time taken to terminate.
The Structure of the 3x + 1 Function
- Papers by Peter Schorer describing several new approaches.
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