1. Virtek Directory :: Science : Math : Number Theory : Open Problems : Collatz Pro Back to the top page of the Virtek directory. Search. Top Science Math Number_Theory Open_Problems collatz_problem http://directory.virtek.com/Directory/Science/Math/Number_Theory/Open_Problems/C

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Make linkRoute your home page Add linkRoute to your favorites Share linkRoute with a friend Web www.linkroute.com Top Science Math Related Categories Categories Description WebSites The Structure of the 3x + 1 Function Papers by Peter Schorer describing several new approaches. http://www.occampress.com/ Collatz 3n+1 Problem Structure Observations posted by Ken Conrow to stimulate further research. http://www-personal.ksu.edu/~kconrow/ Collatz Problem From Eric Weissten's World of Mathematics. Article with references and links. http://mathworld.wolfram.com/CollatzProblem.html The 3x+1 Problem Conference Proceedings Katholische Universit¤t Eichst¤tt, Germany; 56 August 1999. On-line proceedings and group photo. http://www.math.grin.edu/~chamberl/conf.html Computational Verification of the 3x+1 Conjecture Results up to 2^60 by Tom¡s Oliveira e Silva. http://www.ieeta.pt/~tos/3x+1.html The Collatz Problem, Data and Models Properties and predictive models for the Collatz Problem and relative functions. http://site.voila.fr/Collatz_Problem

4. Collatz Problem A problem first posed by the German mathematician Lothar Collatz (19101990) in 1937, that is also known variously as the 3n + 1 problem, Kakutani s problem http://www.daviddarling.info/encyclopedia/C/Collatz_problem.html

NUMBER THEORY A B C ... CONTACT entire Web this site Collatz problem A problem first posed by the German mathematician Lothar Collatz (1910-1990) in 1937, that is also known variously as the 3 n + 1 problem, Kakutani's problem, the Syracuse problem, Thwaites' conjecture, and Ulam's conjecture. It runs as follows. Let n be any integer. (1) If n is odd, put n equal to 3 n + 1; otherwise, put n equal to n /2. (2) If n = 1, stop; otherwise go back to step 1. Does this process always terminate (i.e. end in 1) for any value of n . British mathematician Bryan Thwaites (1996) has offered a £1,000 reward for a resolution of the problem. However, John Conway has shown that Collatz-type problems can be formally undecidable, so it not known if a solution is even possible. The sequences of numbers produced by the Collatz problem are sometimes known as hailstone sequences Reference Guy, Richard K. Unsolved Problems in Number Theory , 2nd ed. New York: Springer-Verlag, 1994. Related category NUMBER THEORY Also on this site: Encyclopedia of History BACK TO TOP var site="s13space1234"

5. BOTW Directory - Science > Math > Number Theory > Open Problems > Collatz Proble Top Science Math Number_Theory Open_Problems collatz_problem Submit Site. The 3x + 1 Problem and its Generalizations Includes problems and questions http://botw.org/top/Science/Math/Number_Theory/Open_Problems/Collatz_Problem/

Directory Submit Site Free Advertising Sign In ... Sponsor This Category Free for 60 Days - Customize your message and appear alongside search results. Start your Free Trial today! Top: Science: Math: Submit Site ... The 3x + 1 Problem and its Generalizations - Includes problems and questions, author biography, and related links. With articles and proceedings of mathematics workshop. The 3x+1 Problem Conference Proceedings - Shows conference schedule, proceedings, and location. Also presents information about the organizers and registration details. An Image from the Collatz Problem - Provides information on the obtaining of the sequence of integers. Also shows an image and related links. The Collatz 3n+1 Conjecture is Unprovable - Shows information of the author, users' comments, and email updates. Also contains references and citations for submission. Collatz 3n+1 Problem Structure - Includes pages on paradoxes, some discussion of Feinstein's proof of the unprovability of the Collatz conjecture, and transition diagrams. Also presents a slide show, and numerous additions and corrections. Collatz Problem - Provides diagrams, sample problems and solutions, and tables. With downloads and comment page for the users.

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Home Art of Problem Solving WOOT! Books ... Log in Collatz Problem From AoPSWiki Define the following function on The Collatz conjecture says that, for any positive integer , the sequence contains 1. This conjecture is still open. Some people have described it as the easiest unsolved problem in mathematics. This article has been found by the AoPSWiki Editors not to be written in wiki style. Help us out by putting this page in wiki style and removing this message. Retrieved from " http://www.mathlinks.ro/Wiki/index.php/Collatz_Problem Categories Articles that need to be wikified Number theory Views Page Discussion View source History Personal tools Log in / create account Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 02:04, 8 October 2007. This page has been accessed 611 times. About AoPSWiki Created and Maintained by Valentin Vornicu - (c) AoPS Inc. 2004-2007

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10. Math: Number Theory: Open Problems: Collatz Problem The Collatz Problem, Data and Models Properties and predictive models for the Collatz Problem and relative functions. http//site.voila.fr/collatz_problem http://www.spacetransportation.org/Math/Number_Theory/Open_Problems/Collatz_Prob

Math: Number Theory: Open Problems: Collatz Problem Home Add Url About Us Contact Us ... Open Problems : Collatz Problem Advertising Links The Structure of the 3x + 1 Function Papers by Peter Schorer describing several new approaches. http://www.occampress.com/ The 3x + 1 Problem and its Generalizations A survey article by Jeff Lagarias. http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/paper.html The 3x+1 Problem Annotated Bibliography By Jeffrey Lagarias, 1997. http://www.research.att.com/~jcl/3x+1.html 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. http://personal.computrain.nl/eric/wondrous/ Experiments with the 3n+1 Sequence An online calculator by Alfred Wassermann. http://did.mat.uni-bayreuth.de/Fun/3np1_e.html Collatz 3n+1 Problem Structure Observations posted by Ken Conrow to stimulate further research. http://www-personal.ksu.edu/~kconrow/ Collatz Problem From Eric Weissten's World of Mathematics. Article with references and links. http://mathworld.wolfram.com/CollatzProblem.html

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Math: Number Theory: Open Problems: Collatz Problem the entire directory only this category Advanced Search Home Math Number Theory ... Open Problems : Collatz Problem LINKS: An Image from the Collatz Problem http://www.onezero.org/collatz.html By Andrew Shapira. The intensity of a point denotes the time taken to terminate. Collatz 3n+1 Problem Structure http://www-personal.ksu.edu/~kconrow/ Observations posted by Ken Conrow to stimulate further research. Collatz Problem http://mathworld.wolfram.com/CollatzProblem.html From Eric Weissten's World of Mathematics. Article with references and links. Experiments with the 3n+1 Sequence http://did.mat.uni-bayreuth.de/personen/wassermann/fun/3np1_e.html An online calculator by Alfred Wassermann. On The 3x + 1 Problem http://personal.computrain.nl/eric/wondrous/ 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 http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/paper.html A survey article by Jeff Lagarias. The 3x+1 Problem Conference Proceedings http://www.math.grin.edu/~chamberl/conf.html

14. RZDirectory Top Science Math Number_Theory Open_Problems collatz_problem. » The Collatz 3n+1 Conjecture is Unprovable A paper by Craig Alan Feinstein arguing http://www.rzdirectory.com/index.php/Science/Math/Number_Theory/Open_Problems/Co

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Login Search Mega Net: Home Library Sciences Mathematics ... Number Theory : Collatz Problem 3x + 1 Problem and its Generalizations Jeffrey C. Lagarias writes this document on the 3x+1 problem also known as Collatz problem and the Syracuse problem. Read an introduction and generalizations. http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/paper.html International Conference on the Collatz Problem International conference discussed the Collatz Problem and related topics. Download papers and abstracts of talks given during the proceedings. http://www.math.grin.edu/~chamberl/conf.html Mathworld - Collatz Problem Author Eric W. Weisstein presents a long and detailed explanation of Collatz Problem with hyperlinks and includes a list of linked references. http://mathworld.wolfram.com/CollatzProblem.html Structure of the 3x + 1 Function http://www.occampress.com/ About Us

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Home Photo Albums Links Maywoods Dates ... DaVinci Creed Only days remaining until Maywoods! collatz problem Science, Math, Number Theory, Open Problems, Collatz Problem Top Science Math - Katholische Universit¤t Eichst¤tt, Germany; 56 August 1999. On-line proceedings and group photo. - A survey article by Jeff Lagarias. - Observations posted by Ken Conrow to stimulate further research. - Papers by Peter Schorer describing several new approaches. - Results up to 2^60 by Tom¡s Oliveira e Silva. - Properties and predictive models for the Collatz Problem and relative functions. - A survey by Keith Matthews [PDF]. - By Andrew Shapira. The intensity of a point denotes the time taken to terminate. - 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. - By Jeffrey Lagarias, 1997. - An online calculator by Alfred Wassermann. - A paper by Craig Alan Feinstein arguing that the Collatz Conjecture cannot be formally proved. - From Eric Weissten's World of Mathematics. Article with references and links.

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