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Collatz Problem: more detail  

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.mathematischebasteleien.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  

43. Heiner Marxen  Busy Beaver In einer Seite Prinzipielle Grenzen der Berechenbarkeit schreibt Arno SchwarzÃ¼ber Turing Maschinen, Busy Beaver und das collatz problem (3n+1). Es gibt http://www.drb.insel.de/~heiner/BB/  

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://atlasconferences.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  

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  

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/knownmath/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/knownmath/98/collatz_catalan  

49. Puzzle 73. A Collatzlike 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  

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  

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/dMathematics/dNumbertheory/b3x 1 
53. !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! !!! Translate this page Antwort *grins*. Schauma mal, wer das zusammengebracht hat Jens lÃ¶st das RÃ¤tselam 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  

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 (EichstÃ¤tt, Germany); http://www.mathsoft.com/mathresources/problems/article/0,,1999,00.html 
56. Index Of /muneer_ilyas/school/Maths Problems/Collatz Problem (Â£1000)_files Index of /muneer_ilyas/school/Maths problems Parent Directory 09Apr2003 0815  collatz problem (Â£10.. 21Mar2003 0414 36kcollatz problem (Â£10.. 21Mar2003 0346  Help files/ 21Mar2003 0406 http://homepage.ntlworld.com/muneer_ilyas/school/Maths problems/Collatz Problem  

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  

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  

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://opensite.org/Science/Mathematics/Number_Theory/Open_Problems/  

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