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Collatz Problem: more detail

Conjectures: P Versus Np Problem, Poincaré Conjecture, Collatz Conjecture, Hilbert's Problems, Catalan's Conjecture, Sierpinski Number
Optimization Problems (Applied Mathematical Sciences) (Volume 0) by L. Collatz, W. Wetterling, 1975-07-23
Numerical Treatment of Free Boundary Value Problems: WORKSHOP NUMER.TREATMEnt Free Bound.Value Probl.Oberwolfach (International Series of Numerical Mathematics) by ALBRECHT, COLLATZ, et all 1982-06-14
Constructive Methods for Nonlinear Boundary Value Problems and Nonlinear Oscillations: CONFERENCE AT THE OBERwolfach Math.Res.Inst.,19.-25.11.1978 (International Series of Numerical Mathematics) by ALBRECHT, COLLATZ, et all 1979-01-01
Numerical Treatment of Eigenvalue Problems, Vol. 3 (International Series of Numerical Mathematics) by ALBRECHT, COLLATZ, et all 1984-05-31
NUMERICAL TREATMENT OF FREE BOUNDARY VALUE PROBLEMS by J.; Collatz, L.; et al; editors Albrecht, 1982
Numerical Treatment of Eigenvalue Problems: Workshop in Oberwafach, February 25-March 3, 1990/Numerische Behandlung Von Eigenwertaufgaben : Tagung (International Series of Numerical Mathematics) by J. Albrecht, Lothar Collatz, et all 1991-05
Numerical Treatment of Eigenvalue Problems (International Series of Numerical Mathematics)
OPTIMIZATION PROBLEMS.Translated by P.Wadsack.*(Applied Mathematical Sciences,17) by L./Wetterling,W. Collatz, 1975-01-01
The Dynamical System Generated by the 3n+1 Function (Lecture Notes in Mathematics) by Günther J. Wirsching, 1998-03-20

lists with details

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/
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

Extractions: 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.
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/

Extractions: /*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 Search SourceForge.net Find Software Collatz Problem Program More by deherlet 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. Mathematics 64-bit MS Windows Other License English Polish Science/Research Console/Terminal wxWidgets C++ Subscribe 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.
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
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 Algorithm
File Format PDF/Adobe Acrobat Quick View
http://www.cdjj.org/miscellany/Collatz_Algorithm.pdf
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
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
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

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

Extractions: 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
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

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

Extractions: 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.
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
[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
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
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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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

Extractions: skip to main skip to sidebar A blog about programming. 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. 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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