Home  - Theorems_And_Conjectures - Collatz Problem

Books Baby Camera Phones Computers Games DVD Electronics Kitchen Magazines Music Garden Software Tools Toys Video Apparel & Accessories Jewelry & Watches Musical Instruments Health & Personal Care Beauty Sports & Outdoors Office Products

e99.com Bookstore

Images

Newsgroups

41-60 of 88    Back | 1  | 2  | 3  | 4  | 5  | Next 20

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

41. Kaprekar Number
    The 3n+1 Problem (collatz problem) top Take any natural number, from whichyou derive a sequence of numbers according to the following rules.  
    http://www.mathematische-basteleien.de/kaprekar.htm

42. Mathematical Problems - Problem Solving - Mathematical Competitions (Math Links
    The 3x+1 problem, also known as the collatz problem, the Syracuse problem, Kakutani sproblem, Hasse s algorithm, and Ulam s problem by Jeff Lagarias;  
    http://mathres.kevius.com/problem.html
    
    Extractions: A collection of simple algebra word problems (SureMath: 21st Century Problem Solving) Algebrator - an Algebra Problem Solver for Students and Teachers ALVIRNE HIGH SCHOOL PROBLEM OF THE WEEK SITE Andrei Jorza's Home Page Calculus Problems Alvirne High School in Hudson, N.H. The Cereal Box Problem by George Reese A Collection of Math-Olympiad-Problems by Hans Vernaeve Competitions Canadian Mathematical Society (CMS) Countries with Mathematical Olympiad Websites - Links to Mathematical Olympiad Websites. CRUX Mathematicorium Online The Digital Supplement to the Canadian Mathematical Society's Problem Solving Journal Ken Duisenberg's Puzzle of the Week Elementary Problem of the Week by Ruth Carver (MathForum) Fermat's Last Theorem Flanders Mathematics Olympiad The Goal Angle Problem Hilbert's Tenth Problem by Karlis Podnieks Paul Erdos: An I nfinity of Problems - Ivars Peterson (MathLand) International Mathematical Olympiad / Olympiade internationale ... International Mathematics Olympiad (IMO) Eindhoven University of Technology Mathematic Olympiad Problems from around the world by Mohammad Katoozian

43. Heiner Marxen - Busy Beaver
    In einer Seite Prinzipielle Grenzen der Berechenbarkeit schreibt Arno Schwarzüber Turing Maschinen, Busy Beaver und das collatz problem (3n+1). Es gibt  
    http://www.drb.insel.de/~heiner/BB/
    
    Extractions: Busy Beaver The function Sigma (n) denotes the maximal number of tape marks which a Turing Machine (TM) with n internal states and a two-way infinite tape can produce onto an initially empty tape and then halt. The function S (n) denotes the maximal number of steps (shifts) which such a TM can do (it needs not produce many tape marks). The following table gives some known values: n Sigma (n) S (n) Source Lin and Rado Lin and Rado Lin and Rado Brady Marxen and Buntrock Marxen and Buntrock Note: The values for n=6 have been verified independently by Paul R. Stevens and by Clive Tooth. The exact numbers are found in the new list of 6-state record machines A general method due to Milton W. Green produces (computable, but not primitive recursive) lower bounds of Sigma for every n. He gives Sigma Of course, if you find an error in the above table, or can extend it... please let me know The author's paper Attacking the Busy Beaver 5 , Bulletin of the EATCS, Number 40, February 1990, pp. 247-251, [ISSN 0252-9742]

44. Atlas: The Relation Between Collatz Conjecture And Primes By Murad A. AlDamen
    the wellknown conjecture ,Collatz conjecture One of many conjectures still withoutproof a problem posed by L. Collatz in 1937 The collatz problem asks if  
    http://atlas-conferences.com/c/a/f/t/16.htm

45. Internet Center For Mathematics Problems
    collatz problem. Famous Problems in Mathematics The Four Colour Theorem;The Trisection of an Angle. Which are the 23 Hilbert Problems?  
    http://www.mathpropress.com/mathCenter.html
    
    Extractions: Sign-in We invite you to visit the MathPro Press home page Many mathematics journals contain problem columns. They invite readers to send in solutions to the problems. The best solution submitted gets printed in a future issue along with the names of all the solvers. We list below only a few of the journals that are currently running problem columns. You are welcome to try your hand at solving these problems. Solutions should be sent to the appropriate problem column editor ( not to MathPro Press).

46. Introduction To Artificial Intelligence Selmer Bringsjord
    Hyperproof file.); A picture of the collatz problem; More on the CollatzProblem and Related Problems; Is English Compositional? (picture  
    http://www.rpi.edu/~brings/intai.html
    
    Extractions: The Intro to AI Show Meet the Cast Video Highlights Handouts ... Supporting Links Problems/Puzzles for Smart Agents Projects Project 3 Finish Shapiro's ELIZA, i.e., (p1). Due by 5pm on day of final exam for studio audience. Due on same day as final for home audience (emailed to Selim as ASCII attachment).

47. From Gerry@mpce.mq.edu.au (Gerry Myerson) Subject Re Is Collatz
    seem to recall that Conway may have established this fact.) Conway defined a familyof problems, a natural generalization of the collatz problem, and showed  
    http://www.math.niu.edu/~rusin/known-math/99/collatz_undec

48. From Robert Harrison Mongrels@streamlinerec. Nospamprestel.co.
    odds. The 2^23^1 = 1 values for s and t is related to the know attractor of the collatz problem the 1- 4- 2- 1 cycle. Robert  
    http://www.math.niu.edu/~rusin/known-math/98/collatz_catalan

49. Puzzle 73.- A Collatz-like Sequence. (A Puzzle Suggested By Jack Brennen )
    This is obviously derived from the collatz problem, and in fact, all even or primenumbers = 3 have the same successor as they do in the Collatz sequence  
    http://www.primepuzzles.net/puzzles/puzz_073.htm
    
    Extractions: Puzzles Puzzle 73.- A Collatz-like sequence. (A puzzle suggested by Jack Brennen Consider the sequence of integers B[] defined by a starting point B[0] and the rules: If B[n] is prime, B[n+1] is defined as 3*B[n]+1. If B[n] is composite, B[n+1] is defined as the largest proper divisor of B[n], which can also be described as B[n]/P, where P is the smallest prime factor of B[n]. The question is this : Does every starting point eventually end up entering the cycle The same question can be posed with the rule changed so that prime numbers go to 3*B[n]-1 instead of 3*B[n]+1. Do all starting points then eventually enter this cycle? Solution Felice Russo got the following interesting results: " Question 1 . I have checked (with an Ubasic program) that all the integers between and terminate in the cycle: 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2. Moreover for the first 1000 integers I calculated the number of steps needed to end up in the cycle. I indicate this quantity with T(n) and we can call it the "transient time". Then I calculated the ratio T(n)/n ("Normalized Transient time") which behavior is reported in the below graph.

50. The Collatz Problem, Also Known As The 3x+1 Problem
    The collatz problem, Also Known as The 3x+1 Problem Ilan Vardi The Collatz mapis taken to be x x/2 if x is even and x - (3x+1)/2 if x is odd.  
    http://www.cs.ucla.edu/~klinger/col.html

51. F. Conjectures (Math 413, Number Theory)
    Conj All integers greater than 1 have occur as multiplicities. (Sierpinski). RefsUnsolved Problems in Number Theory, Guy, 1994, Sect B.37. The collatz 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. Conj: The only zeros of Z( s ) are at s 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 n , is defined by M n n Thm: M n is prime implies that n n is perfect. (Euclid)

52. E. Akin Why Is The 3x+1 Problem So Hard? Math. Magazine (ca.
    Eichsta t Conference 1999, 5p. 13469 Stefan Andrei/Manfred Kudlek/Radu Stefan NiculescuSome results on the collatz problem. Eichsta t Conference 1999, 15p.  
    http://felix.unife.it/Root/d-Mathematics/d-Number-theory/b-3x 1

53. !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!!
    Translate this page Antwort *grins*. Schauma mal, wer das zusammengebracht hat Jens löst das Rätselam 11.3.2003 um 1202 Uhr Es handelt sich dabei um das collatz problem.  
    http://www.astro.univie.ac.at/~strv/Puzzle/old_56.html

54. [The Collatz Problem Or 3n+1 Problem Is As Follows. Take A Natural
    The collatz problem or 3n+1 problem is as follows. Take a natural numbern. If it s even, halve it; if odd, triple it and add one.  
    http://www.hevanet.com/cristofd/brainfuck/collatz.b
    
    Extractions: http://www.hevanet.com/cristofd/brainfuck/)]>,[ [ [ >>>[>>>>]+[[-]+ <, ] [The Collatz problem or 3n+1 problem is as follows. Take a natural number n. If it's even, halve it; if odd, triple it and add one. Repeat the process with the resulting number, and continue indefinitely. If n is 0, the resulting sequence is 0, 0, 0, 0... It is conjectured but not proven that for any positive integer n, the resulting sequence will end in 1, 4, 2, 1... See also http://www.research.att.com/projects/OEIS?Anum=A006577 This program takes a series of decimal numbers, followed by linefeeds (10). The entire series is terminated by an EOF (0 or "no change"). For each number input, the program outputs, in decimal, the number of steps from that number to zero or one, when following the rule above. It's quite fast; on a Sun machine, it took three seconds for a random 640-digit number. One more note. This program was originally written for Tristan Parker's Brainfuck Texas Holdem contest, and won by default (it was the only entry); the version I submitted before the contest deadline is at http://www.hevanet.com/cristofd/brainfuck/oldcollatz.b Daniel B. Cristofani

55. Mathsoft: Mathsoft Unsolved Problems: Unsolved Problems On Other Sites
    also Keith Matthew s The Generalized 3x+1 Mapping (University of Queensland) and1999 Conference on the collatz problem Proceedings (Eichstätt, Germany);  
    http://www.mathsoft.com/mathresources/problems/article/0,,1999,00.html
    
    Extractions: search site map about us  + news  + ... Unsolved Problems Unsolved Problems Links On a Generalized Fermat-Wiles Equation Zero Divisor Structure in Real Algebras Sleeping Habits of Armadillos Mathsoft Constants ... Math Resources Unsolved Problems on Other Sites Jeff Lagarias' 3x+1 problem and related problems The Generalized 3x+1 Mapping (University of Queensland) and 1999 Conference on the Collatz Problem Proceedings Alex Lopez-Ortiz's sci.math FAQ on Famous Problems in Mathematics (University of New Brunswick) Chris Caldwell's Riemann Hypothesis (University of Tennessee at Martin); also Daniel Bump's Riemann Hypothesis (Stanford University) and Barry Cipra's A Prime Case of Chaos MathPro Press Unsolved Math Problem of the Week column and General References Twin Primes Conjecture and Goldbach's Conjecture, discussed in Prime Numbers: Some Unsolved Problems , part of MacTutor History of Mathematics (University of St Andrews); also Chris Caldwell's Prime Conjectures and Open Questions (University of Tennessee at Martin) Jan Otto Munch Pedersen's Known Amicable Pairs (Vejle Business College, Denmark) and Chris Caldwell's

56. Index Of /muneer_ilyas/school/Maths Problems/Collatz Problem (£1000)_files
    Index of /muneer_ilyas/school/Maths problems Parent Directory 09Apr-2003 0815 - collatz problem (£10.. 21-Mar-2003 0414 36kcollatz problem (£10.. 21-Mar-2003 0346 - Help files/ 21-Mar-2003 0406  
    http://homepage.ntlworld.com/muneer_ilyas/school/Maths problems/Collatz Problem
    
    Extractions: Name Last modified Size Description ... Parent Directory 21-Mar-2003 05:04 - book.gif 21-Mar-2003 02:50 1k c2_253.gif 21-Mar-2003 02:55 1k c2_26.gif 21-Mar-2003 02:53 1k c2_39.gif 21-Mar-2003 02:54 1k c2_531.gif 21-Mar-2003 02:55 1k c2_532.gif 21-Mar-2003 02:56 1k c2_533.gif 21-Mar-2003 02:56 1k c2_534.gif 21-Mar-2003 02:57 1k c2_535.gif 21-Mar-2003 02:58 1k c2_536.gif 21-Mar-2003 02:58 1k c2_537.gif 21-Mar-2003 02:59 1k c2_538.gif 21-Mar-2003 03:00 1k c2_539.gif 21-Mar-2003 03:01 1k c2_540.gif 21-Mar-2003 03:03 1k c2_541.gif 21-Mar-2003 03:04 1k c2_542.gif 21-Mar-2003 03:06 1k c2_543.gif 21-Mar-2003 03:07 1k c2_544.gif 21-Mar-2003 03:08 1k c2_545.gif

57. EDUCATION PLANET - 1228 Web Sites For Problem Solving
    12. The 3x+1 problem and its generalizations The 3x+1 problem, also known as thecollatz problem, the Syracuse problem, Kakutani s problem, Hasse s algorithm  
    http://www.educationplanet.com/search/Math/Problem_Solving?startval=10

58. Math Trek: Dangerous Problems, Science News Online, June 29, 2002
    has baffled mathematicians for more than 70 years. Also known as thecollatz problem, it concerns a sequence of positive integers.  
    http://www.sciencenews.org/articles/20020629/mathtrek.asp
    
    Extractions: Week of June 29, 2002; Vol. 161, No. 26 Ivars Peterson Some mathematical problems are easy to describe but turn out to be notoriously difficult to solve. Nonetheless, despite their reputed difficulty and repeated warnings from those who had failed to solve them in the past, these infamous problems continue to lure mathematicians into hours, days, and even years of futile labor. In a presentation this week on "mathematical problems between order and chaos," Jeffrey C. Lagarias of AT&T Labs–Research highlighted three such notorious unsolved problems. His was a cautionary tale, aimed at an audience that included 12 high-school students who had already shown their problem-solving proficiency by topping the 2002 U.S.A. Mathematical Olympiad (USAMO). Susceptible himself to the lure of these tantalizing conundrums, Lagarias admitted that he could have subtitled his talk "some problems I wish I could solve." In recent years, Lagarias has made important research contributions in a variety of mathematical fields, including work on the randomness of pi's digits, number patterns related to circles nested within circles, and the problem of distinguishing knots from unknots. Billiards in triangles In a game of mathematical billiards, a ball moves across a table of a given shape at a constant speed forever. There's no friction to slow the ball down. It simply travels in a straight line until it hits a cushion and rebounds according to the rule that the angle of reflection equals the angle of incidence.

59. Practical Foundations Of Mathematics
    function pList({ a,b})\rightharpoonup N with p( ) = 1, p(cons(a, l)) = a(p(l))and p(cons(b,l)) = b(p(l)). The collatz problem asks whether p is surjective.  
    http://www.dcs.qmw.ac.uk/~pt/Practical_Foundations/html/s62.html
    
    Extractions: Practical Foundations of Mathematics Paul Taylor Free algebraic theories provide a useful ``scaffolding'' which can be used during the building of more complicated linguistic structures, such as dependent type theory in Chapters VIII and IX . In this section we shall describe the recursive aspects of arguments about such structures, which are for example used in the construction of the interpretation functor [[-]]: Cn L S In practice, additional side-conditions are required of the terms which are to be admitted to the language. Some of these, such as the number of arguments taken by each operation-symbol, can be enforced in advance, but others must be stated by simultaneous recursion together with the expressions themselves. The terms which do satisfy the conditions are traditionally known as wffs well formed formulae D EFINITION 6.2.1 A wff-system is a set X of terms for a free theory ( W ar ) such that if r u X j X for all j ar r ]. Therefore parse X TX is a total function on X , and is injective (since ev is a partial inverse).

60. Science: Mathematics: Number_Theory: Open_Problems - Open Site
    23 5 giving A = 1.6299. collatz problem. Also known as the 3n+1 problem,Syracuse problem, Thwaites problem. Define a function on  
    http://open-site.org/Science/Mathematics/Number_Theory/Open_Problems/

41-60 of 88    Back | 1  | 2  | 3  | 4  | 5  | Next 20