21. Collatz Problem Image An Image From the collatz problem http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

22. PlanetMath: Collatz Problem Re Re collatz problem by akrowne on 200110-06 013407. Re Re Re collatz problem Re Re Re collatz problem by atomik_wolf on 2005-03-18 232317 http://planetmath.org/encyclopedia/CollatzProblem.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Collatz problem (Conjecture) We define the function (where excludes zero) such that Then let the sequence be defined as , with an arbitrary natural seed value. It is conjectured that the sequence will always end in , repeating infinitely. This has been verified by computer up to very large values of , but is unproven in general. It is also not known whether this problem is decideable. This is generally called the Collatz problem The sequence is sometimes called the ``hailstone sequence''. This is because it behaves analogously to a hailstone in a cloud which falls by gravity and is tossed up again repeatedly. The sequence similarly ends in an eternal oscillation. "Collatz problem" is owned by akrowne view preamble View style: HTML with images page images TeX source Other names: Ulam's Problem, 1-4-2 Problem, Syracuse problem, Thwaites conjecture, Kakutani's problem, 3n+1 problem

23. Collatz 3n+1 Problem Structure Collatz 3n+1 Problem Structure. As of early April 2005, I've again exhausted what I have to say about the Collatz conjecture, including pages about http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

24. Collatz Problem A problem posed by L. Collatz in 1937, also called Hasse s algorithm, The collatz problem can be simply stated. Starting from a positive integer n, http://www.cs.wpi.edu/~heineman/html/hobbies_/collatz.html

Problem Definition A problem posed by L. Collatz in 1937, also called Hasse's algorithm, Kakutani's problem, Syracuse algorithm, Syracuse problem, Thwaites conjecture, and Ulam's problem (Lagarias 1985). The Collatz problem can be simply stated. Starting from a positive integer n, apply the following function: for even n, coll(n) = n/2 for odd n, coll(n) = (3*n+1)/2 Can you prove or disprove that you will ultimately reach 1. Another way of phrasing this question is to consider the sequence a0, a1, a2, ..., an where a0 is the initial seed for the collatz function and try to find a repeating sequence that does not contain 1 (the only sequence yet found in coll(n) is (2-1-)*. Erdos stated (according to Lagarias) that because of the difficulty in solving this problem, "mathematics is not yet ready for such problems". In other words, don't expect to solve this problem, but have fun trying. Results So Far Consider a sub-sequence n1, n2, ..., nk within a collatz sequence. It is straightforward to construct a sequence of any length that (a) does not contain a cycle; and (b) does not contain the number 1. Lemma 1 . Given positive integer k , there is a number n such that k applications of coll( n ) do not lead to 1.

25. Bookmarks 3xp1 problem syracuse collatz International Conference on the collatz problem and Related Topics collatz problem; 3x+1 problem; total stopping time function. by David Bernier http://perso.wanadoo.fr/jean-paul.davalan/liens/liens_syracuse.html

Accueil Plan du site Bloc notes Jeux ... Home dans la marge University Surf .net Votre portail e-Learning On-Line Encyclopedia of Integer Sequences MaMuX Le Droit de comprendre 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

26. Bookmarks 3xp1 Problem Syracuse Collatz The Collatz (3x+1) Problem Colin Andrew Brady Campbell International Conference on the collatz problem and Related Topics August 56, 1999 Katholische 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.

27. Collatz Problem -- From MathWorld More Collatz Fiction Facts in fact, completely equivalent to the original collatz problem, where every number in the Collatz sequence corresponds with 3 times this number in the http://www.astro.virginia.edu/~eww6n/math/CollatzProblem.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Number Theory Sequences Foundations of Mathematics ... Martinez Collatz Problem A problem posed by L. Collatz in 1937, also called the mapping, conjecture . Let be an integer . Then the Collatz problem asks if iterating always returns to 1 for positive . The members of the sequence produced by the Collatz are sometimes known as hailstone numbers . Conway proved that the original Collatz problem has no nontrivial cycles of length . Lagarias (1985) showed that there are no nontrivial cycles with length . Conway (1972) also proved that Collatz-type problems can be formally undecidable The following table gives the sequences obtained for the first few starting values (Sloane's The numbers of steps required for the algorithm to reach 1 for , 2, ... are 0, 1, 7, 2, 5, 8, 16, 3, 19, 6, 14, 9, 9, 17, 17, 4, 12, 20, 20, 7, ... (Sloane's ; illustrated above). Of these, the numbers of tripling steps are 0, 0, 2, 0, 1, 2, 5, 0, 6, ... (Sloane's

28. The Collatz Problem (3x+1) I was introduced to the collatz problem back in 1990 by Dr. Ashok T. Amin here in the Computer Science Department at the University of Alabama in Huntsville http://hsvmovies.com/static_subpages/personal/math/collatz.html

The Collatz Problem (3x+1) I was introduced to the Collatz problem back in 1990 by Dr. Ashok T. Amin here in the Computer Science Department at the University of Alabama in Huntsville. Dr. Niall Graham, also here in the department, has recently revived my interest in it. The problem deals with sequences of integers generated as follows: Start with a positive integer x > 0. Repeat the following steps: If the last integer in the sequence is 1, stop. The sequence is complete. If the last integer in the sequence is even, divide it by two to get the next integer in the sequence. If the last integer in the sequence is odd, multiply it by three and add one to get the next integer in the sequence. The problem is very simple to state, and the actions are very simple to perform, but the question is, given any starting integer x > 0, will the sequence generated end with the integer 1 in a finite number of steps? Here are the sequences generated for the first few integers: Here is, perhaps, a neater way of showing it: (under construction) As you can see, they all end up at 1. It is interesting to turn this problem around and look at it in reverse, starting with 1 and going in reverse to produce sequences. The reverse of the procedure above is the following:

29. The Complexity Of The Collatz Problem The collatz problem is a very simple, wellknown and unresolved problem of number theory. It can be expressed like this 1. Take any integer number. http://www.geocities.com/CapeCanaveral/Lab/4430/collatz.html

The Complexity of the Collatz problem The Collatz problem is a very simple, well-known and unresolved problem of number theory. It can be expressed like this: 1. Take any integer number. 2. Divide it by 2. If the division is exact, repeat step 2. 3. If it isn't, multiply it by 3, add 1 and go to step 2. For example, if you start with 7, you'll get: The question is: does this journey always end with 1? Computers have calculated this for numbers up to millions, and they've always ended at 1. But it has never been proven it has to be so for every number. Many mathematicians have attacked the problem with no result. Legend says scientists in Los Alamos spent a good deal of their time with it, instead of working in the atomic bomb! It was even rumored it was a Russian sabotage. I haven't solved it, I've got no idea about how to solve it, but I have a good insight of how complex it can be. Let's consider a generalized version of the problem: 1. Take any Gauss integer 2. Divide it by another called a . If the division is exact, repeat step 2. 3. If it isn't, multiply it by

30. Welcome To My Hobby Page The A(x)+y , X/z Page The Collatz Problem There is a math problem attributed to Lothar Collatz that is the interest The 3x + 1 problem, also known as the collatz problem, the Syracuse problem, http://www.geocities.com/ernst_berg@sbcglobal.net/Axyxz.html

Welcome to my Hobby page The A(x)+y , x/z page The Collatz problem has interested me since 1991 It is only fitting to make a page. Sharing is a way of learning Introduction. T here is a math problem attributed to Lothar Collatz that is the interest of many people. The problem, also known as the Collatz problem, the Syracuse problem, Kakutani's problem, Hasse's algorithm , and Ulam's problem http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/links.htm at the Centre for Experimental and Constructive Mathematics hosts a fine example of a collection of data and information. The heart of the system [3x+y , x/2] is iteration based on a number being even or odd . It is suspected that the iteration will result in the value of X looping through the same set of values after some number of iterations. The Collatz system is a Dynamical system The best work I have had a chance to try and understand is a link from A kind reader who sent a link to Barry Brent's fine paper. 3x+1 dynamics on rationals with fixed denominator.

31. Collatz Problem - Information Technology Services Note that collatz problem can be conveniently converted into a decision problem. and if conway did this it means you can never know if collatz problem http://www.physicsforums.com/archive/t-58296_collatz_problem.html

Technology Services Mathematics Number Theory collatz problem loop quantum gravity - collatz problem in mathworld, they say that conway proved "that Collatz-type problems can be formally undecidable." does it mean that this problem is undecidable? if yes i dont know why for example in the website of plus.maths.org they still saying it hasnt been proven/disproven. anyway, i tinkerred around with the original conditions of the problems and instead of when n is even n'=n/2 and when n is odd n'=3*n+1 i decided to switch to when n is even n'=n/2+1 when n is odd n'=2n this sequence is limited from the original because if you start with 2 you get 2 all the way, but besides this and the number 1 (which gives you a repeating sequence of 1,2,1,2....) they yield also a repeating cycle as the one given by the original problem but instead of 4,2,1 cycle you get a 6,4,3 cycle (yes plus two than the original), im not familiar too much to recursion so im not sure if this is a trivial thing. Discuss collatz problem Here, Free! TenaliRaman - collatz problem in mathworld, they say that conway proved "that Collatz-type problems can be formally undecidable."

32. On Collatz Problem - Information Technology Services collatz problem is also based on this invariant symmetry of the Binary Tree, Therefore if there is a general and rigorous proof to collatz problem, http://www.physicsforums.com/archive/t-14886_On_Collatz_Problem.html

Technology Services Physics General Physics Archives ... Theory Development On Collatz Problem Organic - On Collatz Problem 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 Discuss On Collatz Problem Here, Free! matt grime - On Collatz Problem 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.

33. The 3n+1 Collatz Problem The 3n+1 collatz problem. This problem has a mysterious history and it 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

34. CollatzProblem It is also not known whether this problem is decideable. This is generally called the collatz problem. The sequence $ c_n$ is sometimes called the http://202.41.85.103/manuals/planetmath/entries/11/CollatzProblem/CollatzProblem

Collatz problem We define the function (where excludes zero) such that Then let the sequence be defined as , with an arbitrary natural seed value. It is conjectured that the sequence will always end in , repeating infinitely. This has been verified by computer up to very large values of , but is unproven in general. It is also not known whether this problem is decideable. This is generally called the Collatz problem The sequence is sometimes called the ``hailstone sequence''. This is because it behaves analogously to a hailstone in a cloud which falls by gravity and is tossed up again repeatedly. The sequence similarly ends in an eternal oscillation. Contributors to this entry (in most recent order): akrowne As of this snapshot date, this entry was owned by akrowne

35. Collatz Problem - Rechenkraft Translate this page collatz problem. aus Rechenkraft, der freien Wissensdatenbank. Für alle positiven Zahlen N wird die Sequenz S i definiert als http://217.160.138.71/wiki/index.php?title=Collatz_Problem

36. Diskussion:Collatz Problem - Rechenkraft Translate this page Diskussioncollatz problem. aus Rechenkraft, der freien Wissensdatenbank. Erreichbarkeit / Projektstatus? Existiert das Projekt noch? http://217.160.138.71/wiki/index.php?title=Diskussion:Collatz_Problem

37. 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 Related questions and answers Usenet FAQs Search Web FAQs ... RFC Index Send corrections/additions to the FAQ Maintainer: alopez-o@neumann.uwaterloo.ca Last Update June 15 2004 @ 00:31 AM

38. AMCA: The Relation Between Collatz Conjecture And Primes By Murad A. AlDamen One of many conjectures still without proof a problem posed by L. Collatz in 1937. The collatz problem asks if iterating. . 1/2a_n for a_(n1) even http://at.yorku.ca/c/a/f/t/16.htm

Atlas Mathematical Conference Abstracts Conferences Abstracts Organizers ... About AMCA Second International Conference on Smarandache Type Notions In Mathematics and Quantum Physics December 21-24, 2000 University of Craiova Craiova, Romania Organizers Minh Perez (American Research Press, Rehoboth, Box 141, NM 87301, USA), Vasile Seleacu (University of Craiova, Department of Mathematics, Craiova, Romania) View Abstracts Conference Homepage The relation between collatz conjecture and primes by Murad A. AlDamen University of Jerash Before study This conjecture we will recall the will recall the wellknown conjecture ,Collatz conjecture One of many conjectures still without proof a problem posed by L. Collatz in 1937 The Collatz problem asks if iterating 1/2a_n for a_(n-1) even 3*a_(n-1) odd Introduction In these papers I will discuss a new view on a new conjecture "the relation between the primes and Collatz problem " with observe a new distribution of some primes ,also I've tested some of it to be true for all first 1,000,000 numbers but I know it is not enough to be true for all numbers The primes which hold my formula I called it be Murad -Smarandache primes Reference Abstract Before study This conjecture we will recall the will recall the wellknown conjecture ,Collatz conjecture

39. From Gerry@mpce.mq.edu.au (Gerry Myerson) Subject Re Is Collatz defined a family of problems, a natural generalization of the collatz problem, of problems which are natural generalizations of the collatz problem? http://www.math.niu.edu/~rusin/known-math/99/collatz_undec

From: gerry@mpce.mq.edu.au (Gerry Myerson) Subject: Re: Is Collatz Conjecture (3N+1 Problem) Undecidable? Date: Wed, 30 Jun 1999 13:05:01 +1100 Newsgroups: sci.math Keywords: Conway's generalizations include some undecideable problems In article

40. From Bill Daly Billdaly@interport.net Newsgroups Sci.math Subject Reformulation of collatz problem Date Wed, 4 Mar 1998 121004 0500 I have of the collatz problem, which may be of interest to someone. http://www.math.niu.edu/~rusin/known-math/98/collatz_hide

From: "Bill Daly" , Bill Daly

Page 2     21-40 of 102    Back | 1  | 2  | 3  | 4  | 5  | 6  | Next 20