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An Image from the Collatz Problem
- The intensity of a point denotes the time taken to terminate.
Aspects of the Collatz Problem
- Université Louis Pasteur, Strasbourg (France) 6--8 June 2001.
Collatz 3n+1 Problem Structure
- Observations posted by Ken Conrow to stimulate further research.
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 3x+1 Problem Search Results
- Maximum number tested (N): 91·2^50 = 102456891522678784.
The Collatz Problem
- Hundreds of links collected at geometry.net.
The Generalised 3x+1 Problem
- A survey by Keith Matthews.
The Structure of the 3x + 1 Function
- A paper by Peter Schorer describing a new approach to the 3x + 1 Problem and indicating a possible solution.
The Superset Algorithm
- The "limited halting problem": finding machines that solve the halting problem for limited classes of inputs without reporting erroneous results. The Collatz problem is a special case. Software, papers and graphics.
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