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| Top > Science > Math > Number Theory > Open Problems > Collatz Problem |
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The 3x + 1 Problem and its Generalizations - A survey article by Jeff Lagarias. The 3x+1 Problem Annotated Bibliography - By Jeffrey Lagarias, 1997. 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 Generalised 3x+1 Problem - A survey by Keith Matthews. Experiments with the 3n+1 Sequence - An online calculator by Alfred Wassermann. 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. 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. 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, Data and Models - Properties and predictive models for the Collatz Problem and relative functions. The Collatz Problem - Hundreds of links collected at geometry.net. An Image from the Collatz Problem - By Andrew Shapira. The intensity of a point denotes the time taken to terminate. The Generalized 3x+1 Mapping - An unpublished article by Keith Matthews.
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