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  Collatz Problem (11)

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An Image from the Collatz Problem Open in a new windowLink Details
- By Andrew Shapira. The intensity of a point denotes the time taken to terminate.
- http://www.onezero.org/collatz-image

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The 3x + 1 Problem and its Generalizations Open in a new windowLink Details
- An activated-text survey article by Jeff Lagarias.
- http://oldweb.cecm.sfu.ca/organics/papers/lagarias/

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The Collatz 3n+1 Conjecture is Unprovable Open in a new windowLink Details
- A paper by Craig Alan Feinstein arguing that the Collatz Conjecture cannot be formally proved.
- http://arxiv.org/abs/math.GM/0312309

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The 3x+1 Problem Annotated Bibliography Open in a new windowLink Details
- By Jeffrey Lagarias, 1997.
- http://www.math.lsa.umich.edu/~lagarias/3x+1.html

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Experiments with the 3n+1 Sequence Open in a new windowLink Details
- An online calculator by Alfred Wassermann.
- http://did.mat.uni-bayreuth.de/personen/wassermann/fun/3np1_e.html

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The Generalised 3x+1 Problem Open in a new windowLink Details
- A survey by Keith Matthews [PDF].
- http://www.numbertheory.org/pdfs/survey.pdf

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Computational Verification of the 3x+1 Conjecture Open in a new windowLink Details
- Results up to 2^60 by Tomás Oliveira e Silva.
- http://www.ieeta.pt/~tos/3x+1.html

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The 3x+1 Problem Conference Proceedings Open in a new windowLink Details
- Katholische Universität Eichstätt, Germany; 5--6 August 1999. On-line proceedings and group photo.
- http://www.math.grin.edu/~chamberl/conf.html

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Collatz Problem Open in a new windowLink Details
- From Eric Weissten's World of Mathematics. Article with references and links.
- http://mathworld.wolfram.com/CollatzProblem.html

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Collatz 3n+1 Problem Structure Open in a new windowLink Details
- Observations posted by Ken Conrow to stimulate further research.
- http://www-personal.ksu.edu/~kconrow/

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The Structure of the 3x + 1 Function Open in a new windowLink Details
- Papers by Peter Schorer describing several new approaches.
- http://www.occampress.com/

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