21. Collatz Problem Information Sites Reviewed collatz problem sites, by people who know collatz problem and work withcollatz problem. collatz problem From Eric Weissten s World of Mathematics. http://numbersorg.com/NumberTheory/OpenProblems/CollatzProblem/

NUMBERSorg.com Search SPYorg.com (Not sure of spelling? Use first letters and * such as abc* or abcd* or abcde*) Match:.. All Any Format: Long Short Search Words: SPYorg.com METASEARCH Search Words: Top Science Math Number Theory ... Open Problems : Collatz Problem The Structure of the 3x + 1 Function - Papers by Peter Schorer describing several new approaches. 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. 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 3x+1 Problem Conference Proceedings - Katholische Universit¤t Eichst¤tt, Germany; 56 August 1999. On-line proceedings and group photo. The 3x+1 Problem Search Results - Maximum number tested (N): 91·2^50 = 102456891522678784.

22. On Collatz Problem (3n+1) - Technology Services Physics Help and Math Help Physics Forums Mathematics General Math On collatz problem (3n+1). Click Here On collatz problem (3n+1). http://www.physicsforums.com/archive/t-13461

Physics Help and Math Help - Physics Forums Mathematics General Math View Thread : On Collatz problem (3n+1) On Collatz problem (3n+1) Organic Hi, I have 3 questions about Collatz problem: http://mathworld.wolfram.com/CollatzProblem.html If we look at this tree http://michael.cleverly.com/funstuff/3x+1/collatz2.jpg we can see that there are some numbers which are the results of both 3n+1 and n/2, for example: Number 22 is the result of 3*7+1 and also the result of 44/2. Let K be the set off all natural numbers, which are a common result to both 3n+1 and n/2. Edit: I made a mistake, instead of n/2 we have to read m/2 where m not= n. If we want to find a general and rigorous proof of Collatz problem it must be related to all Natural numbers. If the answer to question 1 is yes, then I have 2 more questions: [u]Question 3:[/u] If the answer to Question 2 is no, can we come to the conclusion that Collatz problem is undecidable? Organic Register Now! Free! Talk Science! matt grime [i]Originally posted by Organic [/i] [B]Hi

23. On Collatz Problem - Technology Services View Thread On collatz problem. Click Here On collatz problem. Organic.collatz problem can be found here http//mathworld http://www.physicsforums.com/archive/t-14886

Physics Help and Math Help - Physics Forums Physics General Physics Theory Development View Thread : On Collatz Problem On Collatz Problem Organic Collatz problem can be found here: http://mathworld.wolfram.com/CollatzProblem.html Please look at the attached paper: http://www.geocities.com/complementarytheory/3n1proof.pdf and reply your comments. Thank you, Organic Register Now! Free! Talk Science! matt grime Comments1. k must be fixed one presumes or many things make no sense as we will see. 2. The second line, starting 'A direct convergence', has an extraneous comma that makes it unclear what you mean 5. similarly don't use XOR like that, neither of the 'inputs' is a statement than can be true or false. are those contradictions about k being fixed or not enough for you? probably not. edit: there are also these: what does it mean 'to be out of the range'? why are you misusing decidability like this? godel states that something is undecidable if both it and its negation are consistent with the other axioms. i don't even want to touch the von neumann heirarchy stuff.

24. Mathenomicon.net : Reference : Collatz Problem The collatz problem can be stated as follows Take any . If is odd,set to be . Table 1 Examples illustrating the collatz problem. http://www.cenius.net/refer/display.php?ArticleID=collatzproblem

25. The 3n+1 Collatz Problem The 3n+1 collatz problem. This problem has a mysterious history andit is not easy to explain the attraction of mathematicians for it. http://www.ime.usp.br/~mane/collatz.html

The 3n+1 Collatz Problem This problem has a mysterious history and it is not easy to explain the attraction of mathematicians for it. Consider f(n)=n/2 in n is even and f(n)=(3n+1)/2 if n is odd. It is true that, for all n, the orbit of n by f ends in the cycle (1-2)? The answer for this question is unknown and a lot of problems have borned in the research of this answer (e.g. it is true that the conjecture holds for a set A of positive density? (answer: unknown). Or, if the orbit of n by f is bounded it ends in the cycle (1-2)? (answer: unknown)). We study several aspects of the dynamical system defined by function f and several generalizations of this function. Members Active in this Field (at IME-USP) Manuel Valentim de Pera Garcia - (e-mail mane@ime.usp.br Fabio Armando Tal - (email fabiotal@ime.usp.br Publications A note on the generalized 3n+1 problem - Manuel V. P. Garcia and Fabio A. Tal - Acta Arithmetica XC 3 (1999) pp. 245-250 mane@ime.usp.br Up to research fields in applied math

26. Opening A Selection In An M-File :: Editing And Debugging M-Files (Desktop Tools Debugging ExampleThe collatz problem. The collatz problem is to prove thatthe Collatz function will resolve to 1 for all positive integers. http://www.mathworks.com/access/helpdesk/help/techdoc/matlab_env/edit_d21.html

Desktop Tools and Development Environment Opening a Selection in an M-File You can open a subfunction, function, file, variable, or Simulink model from within a file in the Editor/Debugger. Select the name and then right-click and select Open Selection from the context menu. Based on what the selection is, the Editor/Debugger performs a different action. Selection Action Subfunction Cursor moves to the subfunction within the current M-file. If no subfunction by that name is found in the current M-file, the Editor/Debugger runs the open function on the selection, which opens the selection in the appropriate tool, as shown for the other selection types in this table. M-file or other text file Opens in the Editor. Figure file ( .fig Opens in a figure window. Variable Opens in the Array Editor. Model Opens in Simulink. Other If the selection is some other type, Open selection looks for a matching file in a private directory in the current directory and performs the appropriate action. After selecting a name, you can also choose Help on Selection from the context menu to see documentation for the item. For example, select a function, right-click and select

27. Incremental Search :: Editing And Debugging M-Files (Desktop Tools And Developme an example. Closing MFiles, Debugging ExampleThe collatz problem,© 1994-2004 The MathWorks, Inc. - Trademarks - Privacy Policy. http://www.mathworks.com/access/helpdesk/help/techdoc/matlab_env/edit_d20.html

Desktop Tools and Development Environment Increm ental Search With the incremental search feature, the cursor moves to the next or previous occurrence of the specified text in the current file. It is similar to the Emacs search feature. Incremental search is also available in the Command Windowsee Incremental Search . To use the incremental search feature in the Editor/Debugger. Position the cursor where you want the search to begin. How you begin the incremental search depends on your setting for the Editor/Debugger key bindings preference and in which direction you want to search: Press Ctrl+S to search forward or Ctrl+R to search backward for Emacs and Macintosh key binding (for Macintosh key bindings, use the Command key instead of Ctrl Press Ctrl+Shift+S to search forward or Ctrl+Shift+R to search backward for Windows key bindings (for Macintosh key bindings, use the Command key instead of Ctrl An incremental search field appears in the left side of the status bar of the current file window. F Inc Search means search F orward from the cursor.

28. Zeal.com - United States - New - Library - Sciences - Mathematics - Number Theor A great resource for United States New - Library - Sciences - Mathematics - NumberTheory - Problems Relations - collatz problem. collatz problem Preview http://zeal.com/category/preview.jhtml?cid=10037107

29. Collatz Problem Was Solved And Published: June 29, 2003 : Application HENs Semin http://www.crt.or.jp/~kokochi/CollatzProblem.htm

this page cannot be displayed. Another page for printing So, click here , please.

30. Index Page Of HENs (the New Symmetrical Notation Systems) Seminar new Using HEN3, collatz problem is solved. Back to the Top of this Page. Indexof this Page. 3. Application of the HEN systems. collatz problem is solved. http://www.crt.or.jp/~kokochi/HENindxe.htm

Top Page / Index Page Japanese Page The English Pages are under construction. If you are using a Web Browser, which can handle LAYERs (ex. Navigator 4.0 you can enjoy some pages that explain the Notation Systems by principle movement. Integer table was newly built Text-Book (in Japanese) of this Seminar was published WANTed Cooperators, translating from Japanese to any other Languages. A Digital Balance of system is published. new Using HEN3, Collatz Problem is solved. Back to the Top of this Page Index of this Page 1. Comparison of some Notation systems Notation system using a digital Balance Explanatory notes of digital Balance some Notation systems the Decimal system : Radix = 10 the New Notation systems : Radix = 2, 3, 5, 7 Comparison of same Radix Notation systems Relation between a mixed decimal value and a position on the number line 2. Integer Table / HEN3 / HEN5 / HEN7 / DECimal 3. Application of the HEN systems Collatz Problem is solved. Back to the Index of this Page 1. Comparison of some Notation systems Notation system using a digital Balance Explanatory notes of digital Balance Back to the Index of this Page some Notation systems the Decimal system Arabic numeral system Roman numeral system Japanese abacus (Yotsu-dama abacus) ... Positive Radix Notation systems need minus (or plus) sign.

31. Collatz Problem collatz problem. Thwaites (1996) has offered a 1000 reward for resolving the Conjecture.Let be an Integer. Then the collatz problem asks if iterating, (1). http://icl.pku.edu.cn/yujs/MathWorld/math/c/c433.htm

Collatz Problem A problem posed by L. Collatz in 1937, also called the x +1 Mapping Hasse's Algorithm Kakutani's Problem ... Thwaites Conjecture , and Ulam's Problem (Lagarias 1985). Thwaites (1996) has offered a 1000 reward for resolving the Conjecture . Let be an Integer . Then the Collatz problem asks if iterating always returns to 1 for Positive . This question has been tested and found to be true for all numbers (Leavens and Vermeulen 1992), and more recently, (Vardi 1991, p. 129). The members of the Sequence produced by the Collatz are sometimes known as Hailstone Numbers Negative numbers are included, there are four known cycles (excluding the trivial cycle): (4, 2, 1), ( ), and ( ). The number of tripling steps needed to reach 1 for , 2, ... are 0, 0, 2, 0, 1, 2, 5, 0, 6, ... (Sloane's The Collatz problem was modified by Terras (1976, 1979), who asked if iterating always returns to 1 for initial integer value . If Negative numbers are included, there are 4 known cycles: (1, 2), ( ), and ( ). It is a special case of the ``generalized Collatz problem'' with , and . Terras (1976, 1979) also proved that the set of

32. Editing And Debugging M-Files (Development Environment) Debugging Example The collatz problem. The collatz problem is to prove thatthe Collatz function will resolve to 1 for all positive integers. http://www.math.mcgill.ca/sysdocs/matlabr12/help/techdoc/matlab_env/edit_15a.htm

Development Environment Debugging Example - The Collatz Problem The example debugging session requires you to create two M-files, collatz.m and collatzplot.m , that produce data for the Collatz problem. For any given positive integer, n , the Collatz function produces a sequence of numbers that always resolves to 1. If n is even, divide it by 2 to get the next integer in the sequence. If n is odd, multiply it by 3 and add 1 to get the next integer in the sequence. Repeat the steps for the next integer in the sequence until the next integer is 1. The number of integers in the sequence varies, depending on the starting value, n The Collatz problem is to prove that the Collatz function will resolve to 1 for all positive integers. The M-files for this example are useful for studying the problem. The file collatz.m generates the sequence of integers for any given n . The file collatzplot.m calculates the number of integers in the sequence for any given n and plots the results. The plot shows patterns that can be further studied. Following are the results when n is 1, 2, or 3.

33. Reformulation Of Collatz Problem Reformulation of collatz problem. 4 Mar 1998 Reformulation of collatz problem,by Bill Daly 8 Mar 1998 Re Reformulation of collatz problem, by Dave Rusin http://mathforum.org/epigone/sci.math.research/glexlooye

a topic from sci.math.research Reformulation of Collatz Problem post a message on this topic post a message on a new topic 4 Mar 1998 Reformulation of Collatz Problem , by Bill Daly 8 Mar 1998 Re: Reformulation of Collatz Problem , by Dave Rusin The Math Forum

34. More Collatz Fiction & Facts 3 + 3) / 2 if S i1 is odd It can easily be shown that this (3x+3) sequence is,in fact, completely equivalent to the original collatz problem, where every http://huizen.dto.tudelft.nl/deBruijn/programs/collatz.htm

This is an outstanding unsolved SPAM(*) anyway. And yes, I have found kind of a " solution " for the problem, though it may seem much less satisfactory than most people would like it to be. The gist of my "solution" is that the (3x+1) Conjecture is not a Theorem within the whole number system, at all . Instead, it's just a Statistical Property , which has a multitude of mappings, even within the real numbers, that is: outside the integers. Maybe this is all that has to be said about the infamous Conjecture: that it is not very interesting , in the end. Herewith I mean that its contribution to Number Theory may be of NULL value. But Probability Theory is another story. probably ;-) Yes, I think the major hurdle to be taken is the idea: that the Theory of Probability can yet be used as a proper description, of processes which are quite Deterministic in nature ! (Meanwhile claiming that I am Not the first one who says this) *) Sample of Pure Applicable Mathematics Modified definition To begin with, the definition of the problem (by Eric Roosendaal) will be modified slightly, as follows:

35. Bookmarks 3xp1 Problem Syracuse Collatz superLagarias.html The Collatz (3x + 1) Problem Ilan Vardi http//www.mathsource.com/Content/Applications/Mathematics/0200305 collatz problem http//www http://perso.wanadoo.fr/patrick.davalan/Liens/liens_syracuse.html

3x+1, Collatz, Syracuse Problem Pages Web Livres Papiers Journaux ... Liens Avertissement : PAGES WEB The 3x+1 problem and its generalizations On the 3x+1 problem By Eric Roosendaal Glide Records Table. Delay Records Table residues page completeness page ... Super-Index of The 3x+1 Problem and its generalizations This index was automatically generated using a new tagging program written by Simon Plouffe at the CECM, Simon Fraser University. The Collatz (3x + 1) Problem Ilan Vardi Collatz Problem The Collatz (3x+1) Problem Colin Andrew Brady Campbell The 3x+1 Problem The Collatz Problem (3x+1) Evans A Criswell wondrous On The 3x + 1 Problem Unsolved problems 5x+1 and 7x+1 search results ... The Collatz (3x+1) Problem DEMOS on-line javascript Collatz trajectory calculato Mathematical mysteries - Hailstone sequences Hailstone Evaluator Embedding the 3x+1 Conjecture in a 3x+d Context Edward G. Belaga Maurice Mignotte LIVRES - BOOKS Unsolved Problems in Number Theory (Problem Books in Mathematics, Vol 1) by Richard K. Guy DOCUMENTS - PAPERS Collatz Problem Ken Monks's Faculty-Student Research Program Information A Distributed Search Program for the 3x+1 problem. Gary T. Leavens Computer Science Technical Reports A heuristic argument.

36. Bookmarks 3xp1 problem syracuse collatz 3x+1, Collatz, Syracuse Problem. collatz problem. http//www.astro.virginia.edu/~eww6n/math/CollatzProblem.html The 3x+1 Problem. http://perso.wanadoo.fr/jean-paul.davalan/liens/liens_syracuse.html

Accueil English Plan du site Bloc notes ... .net Votre portail e-Learning 3x+1, Collatz, Syracuse Problem SOMMAIRE Pages Web Maths Demos ... Liens 3x+1 problem applet Cliquer Voir aussi la Page d'origine de l'applet Paragraphe DEMOS PAGES WEB The 3x+1 problem and its generalizations Computational verification of the 3x+1 conjecture Computational projects On the 3x+1 problem By Eric Roosendaal Glide Records Table. Delay Records Table residues page completeness page ... Super-Index of The 3x+1 Problem and its generalizations This index was automatically generated using a new tagging program written by Simon Plouffe at the CECM, Simon Fraser University. The Collatz (3x + 1) Problem Ilan Vardi Collatz Problem The 3x+1 Problem The Collatz Problem (3x+1) Evans A Criswell On the 3x+1 problem By Eric Roosendaal Unsolved problems Ken Monks's FSRP Page Things of interest to number theorists The Collatz (3x+1) Problem ... The Superset Algorithm By M.Najtiv Collatz 3n+1 Problem Structure Ken Conrow Computations on the 3 n + 1 conjecture Worksheet created by Michael Monagan, Text taken from Collatz.tex, Gaston H. Gonnet, Informatik E.T.H. Zurich, Switzerland The Collatz problem, Also Known as The 3x+1 Problem

37. »»Collatz Problem Movie Reviews«« collatz problem Movie Reviews. Related Subjects Math. Family movie reviewsfor collatz problem sorted by average review score NASA Vol. http://www.family-movie-review.com/Science/Math/Collatz_Problem/

Collatz Problem Movie Reviews Related Subjects: Math Family movie reviews for "Collatz Problem" sorted by average review score: NASA - Vol. 1: The Eagle Has Landed/Houston, We've Got a Problem/Apollo 15/Apollo 16 Released in DVD by Madacy Entertainment (01 April, 1999) MPAA Rating: NR (Not Rated) Average review score: Original NASA film of the Apollo missions to the moon This DVD features four original NASA films covering the missions of Apollo 11, 13, 15, and 16, and I found the material quite interesting. A lot of people run Madacy Entertainment into the ground for putting out inferior DVDs, but I don't find this offering inferior at all. Certainly, the documentaries look grainy and old, and the sound is far from crisp, but that all comes from the fact that these are all original NASA films, and anyone who has ever watched Neil Armstrong's first step on the moon knows how bad the picture quality of these historic video recordings are. Madacy also does more than just throw the old films together for this release; included here are a clip of President Kennedy speaking about the space program, biographies of four select astronauts, mission summaries of three Gemini missions and a look at the Gemini capsule (which I admit is rather weird since this DVD covers only the Apollo missions), and a handful of NASA trivia questions. Both informative and entertaining, this collection of vintage NASA films makes for an excellent addition to any space enthusiast's DVD collection. It especially helps those of us too young to actually remember the Apollo missions to understand just how incredible, exciting, and monumental these manned missions to the moon really were.

38. Numcom08 NUMBERS AND COMPUTERS (8) by Albert N. Debono THE collatz problem. Takeany positive number. If it is odd, multiply it by three and add one. http://www.eng.um.edu.mt/~andebo/numbers/numcom08.htm

NUMBERS AND COMPUTERS (8) by Albert N. Debono THE COLLATZ PROBLEM Take any positive number. If it is odd, multiply it by three and add one. If it is even divide it by two. Repeat the process on the new number so obtained and keep on repeating this procedure. Starting with the number 3 we get: 3, 10, 5, 16, 8, 4, 2, 1. If we keep on repeating the procedure after the 1 we would of course get 4, 2, and 1 again ad infinitum i.e. we entered a loop. Thus the number 3 is brought down to 1 in 7 steps and reaches a maximum of 16. If we start with the number 27 instead of 3 we find that we need 111 steps to come down to 1 and a maximum of 9232 will be reached in the sequence. Write a program on your micro which when given a number will output the number of steps required to bring it down to 1 and also the maximum reached. The output could look like this: 27 closes in 111 steps and reaches a maximum of 9232 255 closes in 47 steps and reaches a maximum of 13120 447 closes in 97 steps and reaches a maximum of 39364 It is interesting to see a graphical representation of these sequences by writing a program on your micro so that the numbers generated in the sequence are plotted (vertically) against the step number (horizontally) and the resulting points (joined by straight lines) shown on the monitor.

39. Sci.math FAQ: Unsolved Problems collatz problem * Goldbach s conjecture * Twin primes conjecture _Names of large numbers http://www.faqs.org/faqs/sci-math-faq/unsolvedproblems/

Usenet FAQs Search Web FAQs Documents ... RFC Index sci.math FAQ: Unsolved Problems There are reader questions on this topic! Help others by sharing your knowledge Newsgroups: sci.math alopez-o@neumann.uwaterloo.ca hv@cix.compulink.co.uk (Hugo van der Sanden): To the best of my knowledge, the House of Commons decided to adopt the US definition of billion quite a while ago - around 1970? - since which it has been official government policy. dik@cwi.nl (Dik T. Winter): The interesting thing about all this is that originally the French used billion to indicate 10^9, while much of the remainder of Europe used billion to indicate 10^12. I think the Americans have their usage from the French. And the French switched to common European usage in 1948. gonzo@ing.puc.cl alopez-o@barrow.uwaterloo.ca Rate this FAQ N/A Worst Weak OK Good Great Current Top-Rated FAQs Are you an expert in this area? Share your knowledge and earn expert points by giving answers or rating people's questions and answers! This section of FAQS.ORG is not sanctioned in any way by FAQ authors or maintainers. Questions strongly related to this FAQ: what are some unsolved problems by Dylan McDonald (11/3/2003) Choose 4 prime numbers such that adding the first of them equals the fourth, for example:...

40. Newsgroups Sci.math,sci.answers,news.answers Path Senator * collatz problem * Goldbach s conjecture * Twin primes conjecture _Names of large numbers http://www.faqs.org/ftp/usenet/news.answers/sci-math-faq/unsolvedproblems

Newsgroups: sci.math,sci.answers,news.answers Path: senator-bedfellow.mit.edu!bloom-beacon.mit.edu!spool.mu.edu!torn!watserv3.uwaterloo.ca!undergrad.math.uwaterloo.ca!neumann.uwaterloo.ca!alopez-o From: alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz) Subject: sci.math FAQ: Unsolved Problems Summary: Part 18 of many, New version, Originator: alopez-o@neumann.uwaterloo.ca Message-ID:

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