61. Collatz Problem Article on Collatz Problem Then let the sequence be defined as , with an arbitrary natural seed value. http://myyn.org/m/article/collatz-problem/

62. Re: Collatz Problem: An Idea For Its Solution. So although your heuristic argument is true, it doesn't guarantee that you will reach your termination point. As far as I can tell, you indicate that it might be the case that http://sci.tech-archive.net/Archive/sci.math/2005-05/msg02527.html

Re: Collatz Problem: An idea for its solution. From : "A. Boom" < Date : Thu, 12 May 2005 20:50:51 -0400 Here's something else to consider: does the above work if the sequence is a loop? For example, in the 3n+1271069 system, if you start at 97, after 315529 iterations you find yourself back at 97. So although your heuristic argument is true, it doesn't guarantee that you will reach your termination point (which in this case would be 1271069). I'm not sure what idea is represented by "the 3n+1271069" system. Is it like the clock where after you add so many hours, 12, you are back where you started? If so, how does that enter the Collatz Problem? As far as I can tell, you indicate that it might be the case that an odd number will be encountered, and then, at a later point, the same odd number will be encountered again. This never seems to occur in the sequences that my program has made and certainly would prove the Collatz Problem is not true. Adam. . Follow-Ups Re: Collatz Problem: An idea for its solution. From: References Collatz Problem: An idea for its solution.

63. Collatz Problem Program | Download Collatz Problem Program Software For Free At May 18, 2010 Get Collatz Problem Program at SourceForge.net. Fast, secure and free downloads from the largest Open Source applications and software http://sourceforge.net/projects/collatzproblem/

/*jslint onevar: false, nomen: false, evil: true, css: true, plusplus: false, white: false, forin: true */ /*global unescape, window, jQuery, $, net, COMSCORE */ Welcome, Guest! Log In Create Account Find and develop open source software Find Software ... About Search SourceForge.net Find Software Collatz Problem Program Share More Collatz Problem Program planning by deherlet Summary Files Support ... Develop Program for solve Collatz problem. View all files http://collatzproblem.sourceforge.net You seem to have CSS turned off. Please don't fill out this field. You seem to have CSS turned off. Please don't fill out this field. Separate each tag with a space. Features: GUI (Planned) and Console Interface Bignums (Planned) For Windows (32 (Planned) and 64), Linux, and maybe other Topic: Mathematics Operating System: 64-bit MS Windows License: Other License Translations: English Polish Intended Audience: Science/Research User Interface: Console/Terminal wxWidgets Programming Language: C++ Registered: Subscribe Ratings and Reviews Be the first to post a text review of Collatz Problem Program. Rate and review a project by clicking thumbs up or thumbs down in the right column.

64. Digital Trivia » State Of The Collatz Problem The Collatz problem, sometimes also referred to as the 3x+1 problem is an unsolved conjecture in mathematics. Lothar Collatz proposed it more than 70 years http://blog.haynberg.de/?p=429&lang=en

65. Collatz Problem I was looking at this for fun today and noticed probably something that is Basicaly the http://sci.tech-archive.net/Archive/sci.math/2006-05/msg05093.html

Collatz problem From : "Abstract Dissonance" < Date : Thu, 25 May 2006 18:02:22 -0500 I was looking at this for fun today and noticed probably something that is completely obviously but I just wanted to run it by you guys and see whats going on about it. Basicaly the "tail" of one sequence always seems to end up being another sequence. I've did some simulations and it seems that I can always find a b such that the sequence of b is exactly the same as the sequence of a except with a attached to b. i.e., Not sure if this is always the case but has worked for several that I have tested. It would seem that if this is true one could always get to 1 because you could find a chain of integers that would be descending in size... in essense it would be equivilent to building up the integers by using the "inverse" collatz map and you could get them all. Just curious. Probably would be just has hard to prove as the original problem. Thanks, Jon Follow-Ups Re: Collatz problem From: Abstract Dissonance Re: Collatz problem From: Prev by Date: Re: Another_ p^(2^k), Karzeddin's like Conjecture

66. Collatz Algorithm File Format PDF/Adobe Acrobat Quick View http://www.cdjj.org/miscellany/Collatz_Algorithm.pdf

67. On Collatz Problem On Collatz Problem General Physics discussion Collatz problem can be found here http//mathworld.wolfram.com/CollatzProblem.html http://www.physicsforums.com/showthread.php?t=14886

68. The Collatz Problem Over 2~adic Integers File Format PDF/Adobe Acrobat http://repository.aichi-edu.ac.jp/dspace/bitstream/10424/641/1/kenshi52511.pdf

69. F. Conjectures (Math 413, Number Theory) This conjecture is variously referred to as the Collatz problem (for the original worker in the field), the Syracuse problem, or the 3 x +1 problem. http://www.math.umbc.edu/~campbell/Math413Fall98/Conjectures.html

F. Conjectures Number Theory, Math 413, Fall 1998 A collection of easily stated number theory conjectures which are still open. Each conjecture is stated along with a collection of accessible references. The Riemann Hypothesis Fermat Numbers Goldbach's Conjecture Catalan's Conjecture ... The Collatz Problem The Riemann Hypothesis Def: Riemann's Zeta function, Z(s), is defined as the analytic extension of sum n infty n s Thm: Z( s )=prod i infty p i s , where p i is the i th prime. Thm: The only zeros of Z( s ) are at s s Conj: The only zeros of Z( s ) are at s =-2, -4, -6, ... and on the line Re( s Thm: The Riemann Conjecture is equivalent to the conjecture that for some constant c x )-li( x c sqrt( x )ln( x where pi( x ) is the prime counting function. Refs: Unsolved Problems Elementary Number Theory http://www.utm.edu/research/primes/notes/rh.html (notes in Chris Caldwell's Prime Pages) http://match.stanford.edu/rh/ (Dan Bump's notes) Def: n is perfect if it is equal to the sum of its divisors (except itself). Examples are 6=1+2+3, 28, 496, 8128, ... Def: The n th Mersenne Number, M

70. Collatz Problem News282 Comprehensive facts in respect to collatz problem. You may discover some intelligence in respect to news282 here as well . http://mitglied.multimania.de/mdxlhtb/collatz-problem.html

71. An Artificial Life View To The Collatz Problem File Format PDF/Adobe Acrobat Quick View http://mitpress.mit.edu/books/chapters/0262290758chap75.pdf

72. Collatz Problem 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). http://www.math.sdu.edu.cn/mathency/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

73. Collatz Problem [Archive] - Physics Forums 15 posts 4 authors - Last post Jan 5Note that Collatz problem can be conveniently converted into a decision problem. That is given a number , decide whether it will converge to http://www.physicsforums.com/archive/index.php/t-58296.html

Physics Forums Mathematics Number Theory PDA View Full Version : collatz problem MathematicalPhysicist Jan1-05, 05:09 AM 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. TenaliRaman Jan1-05, 05:51 AM

74. ω-rewriting The Collatz Problem by G Scollo 2004 - Cited by 1 - Related articles http://portal.acm.org/citation.cfm?id=1227085.1227119

75. Editing And Debugging M-Files (Development Environment) Debugging ExampleThe Collatz Problem. The example debugging session requires you to create two Mfiles, collatz.m and collatzplot.m, that produce data for the Collatz problem. http://www-rohan.sdsu.edu/doc/matlab/techdoc/matlab_env/edit_d21.html

Development Environment Debugging ExampleThe 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 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 integer and plots the results. The plot shows patterns that can be further studied. Following are the results when n is 1, 2, or 3.

76. Open Questions And Tough Answers - Numericana Apr 14, 2007 (200212-21) The Collatz Problem Collatz sequences are sequences of integers where an even N is followed by N/2 and an odd N by 3N+1. http://www.numericana.com/answer/open.htm

home index units counting ... physics Open Questions or Tough Answers , Ph.D. It is not because things are difficult that we do not dare, it is because we do not dare that they are difficult. Seneca (5 BC - AD 65) As our island of knowledge grows, so does the shore of our ignorance John Wheeler (Scientific American, 1992) The famous problems discussed below are either still unsolved or remained open for quite a while, in spite of considerable scrutiny. Some entail substantial cash rewards The Riemann Hypothesis z P = NP ? Can we find in polynomial time what we can check that fast? Collatz sequences go from n to n/2 or (3n+1)/2. Do they all lead to 1? (1904). Proven by Grisha Perelman in 2002. Fermat's Last Theorem (1637). Proven by Andrew Wiles in 1995. Open questions mentioned elsewhere on this site: Odd Perfect Numbers : Arguably, the oldest unsolved mathematical question. Related articles on this site: Parodies and hoaxes Scientific Mysteries : The Unexplained. Cosmology 101 : Basic concepts for studying the Universe as a whole. Related Links (Outside this Site) What's New ? by Terence Tao Open Questions in Physics by John Baez MathPages Wanted List by Kevin S. Brown

77. [hal-00129730, V1] The Collatz Problem And Its Generalizations File Format PDF/Adobe Acrobat Quick View http://hal.archives-ouvertes.fr/docs/00/12/97/30/PDF/06018.pdf

78. International Conference On The Collatz Problem International Conference on the Collatz Problem and Related Topics August 56, 1999 Katholische Universit t Eichst tt, GERMANY; This conference is intended for anyone http://www.math.grinnell.edu/~chamberl/conf.html

International Conference on the Collatz Problem and Related Topics August 5-6, 1999 This conference is intended for anyone interested in the 3x+1 problem ( also known as the Syracuse algorithm, Collatz', Kakutani's, or Ulam's problem), and related mathematics. CONFERENCE SCHEDULE CONFERENCE PROCEEDINGS E-mail: xhillner@aol.com Phone: (08421) 982010 Fax : (08421) 982080 You may also want to see other places of accomodation ; click on the word "Tourist Info" and then "Hotels". REGISTRATION: US$60 or 54 Euro, payable at the conference. FINANCIAL SUPPORT: A limited amount of financial support may be available. The Willibaldsburg (castle) St. Peter's Dominican Church ORGANIZERS: Marc Chamberland Department of Mathematics Grinnell College Grinnell, Iowa 50112 U.S.A. Office: (515) 269-4207 Fax: (515) 269-4984 chamberl@math.grin.edu Germany Telefon: (08421) 93-1456 Telefax: (08421) 93-1789 guenther.wirsching@ku-eichstaett.de

79. Walking Cautiously Into The Collatz Wilderness Algorithmically File Format Microsoft Powerpoint View as HTML http://www-irma.u-strasbg.fr/~belaga/a8*BelagaMathInfo06Presentation060920.ppt

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80. Programming During Recess: Collatz Numbers (Project Euler Problem 14) Mar 24, 2010 Problem 14 of Project Euler deals with the Collatz conjecture. In particular, how long does it take for a particular integer to be reduced http://jdfrens.blogspot.com/2010/03/collatz-numbers-project-euler-problem.html

skip to main skip to sidebar Programming During Recess A blog about programming. Wednesday, March 24, 2010 Collatz Numbers (Project Euler Problem 14) Problem 14 of Project Euler deals with the Collatz conjecture . In particular, how long does it take for a particular integer to be reduced to 1? Here's my solution in Erlang: This is what I'm calling a "Collatz number". Problem 14 is to find the number less than a million which has the largest Collatz number. If a problem screamed " Memoization ", this is it. Except that it shouldn't. It does help (which we'll get to), but it turns out to not be necessary. Brute Force Solution To find the maximum Collatz number in Erlang, I used this function (with the one above): seq(1,N) returns a list of integers. The function I map over this list returns a tuple of both the original number and its Collatz number. I need to take the maximum over the Collatz numbers, but I need to return the original number. Erlang's tuple data-structure is really helpful here; I love how tuples are ordered (as they are in Haskell). There are many ways in which this should be really inefficient. First, the original collatz(N) function repeats a lot of computations: to compute collatz(32), it would be helpful if I already know collatz(16). And to compute collatz(5), it

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