3x+1, Collatz, Syracuse Problem

3x+1 problem applet

Cliquer l'intérieur du cadre de l'applet pour changer d'élément.

Voir aussi la Page d'origine de l'applet (Paragraphe DEMOS)

PAGES WEB

<http://www.multimania.com/ericmer/syracuse/syracuse.htmLa conjecture de Syracuse>
The 3x+1 problem and its generalizations

Jeff Lagarias AT&T Bell Laboratories Murray Hill, New Jersey
<http://www.cecm.sfu.ca/organics/papers/lagarias/index.html>
Computational verification of the 3x+1 conjecture

TomÃ¡s Oliveira e Silva Computational projects
<http://www.ieeta.pt/~tos/3x+1.html>
On the 3x+1 problem

By Eric Roosendaal

Glide Records Table. Delay Records Table residues page completeness page Completeness Records Table Class Records Table Path Records Table
<http://oldpersonal.computrain.nl/eric/wondrous/index.html>
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.
<http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/superLagarias.html>
The Collatz (3x + 1) Problem

Ilan Vardi
<http://www.mathsource.com/Content/Applications/Mathematics/0200-305>
Collatz Problem
<http://www.astro.virginia.edu/~eww6n/math/CollatzProblem.html>
The 3x+1 Problem
<http://www.math.grin.edu/~chamberl/3x.html>
The Collatz Problem (3x+1)

Evans A Criswell
<http://mickey.cs.uah.edu/~criswell/collatz.html>
On the 3x+1 problem

By Eric Roosendaal
<http://194.178.35.44/eric/wondrous/index.html>
Unsolved problems
<http://abel.math.umu.se/~frankw/unsolved.html>
Ken Monks's FSRP Page
<http://seawolf.uofs.edu/~monks/fsrp.html>
Keith Matthews' 3x+1 page

Homepage of Keith Matthews, Generalized 3x+1 mappings, The generalized 3x+1 mapping: George Leigh's approach
<http://www.numbertheory.org/3x+1/>
The Collatz (3x+1) Problem
<http://www.ug.cs.dal.ca/~campbell/collatz.html>
The Superset Algorithm

By M.Najtiv
<http://www8.pair.com/mnajtiv/halt/halt.html>
Collatz 3n+1 Problem Structure

Ken Conrow
<http://www-personal.ksu.edu/~kconrow/index.html>

MATHÉMATIQUES - MATHEMATICS

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
<http://www.mapleapps.com/categories/mathematics/numbertheory/html/collatz.html>
The Collatz problem, Also Known as The 3x+1 Problem

Ilan Vardi
<http://mathsource.wri.com/MathSource22/Applications/Mathematics/0200-305/Collatz.m>

DEMOS

Vol

Ã©chelle logarithmique et/ou sÃ©quences courtes possibles
<http://perso.wanadoo.fr/jean-paul.davalan/divers/syracuse/index.html>
on-line javascript Collatz trajectory calculato
<http://mathstat.math.carleton.ca/~amingare/mathzone/3n+1.html>
Mathematical mysteries - Hailstone sequences

Hailstone Evaluator
<http://pass.maths.org.uk/issue1/xfile/index.html>
Cut The Knot!

An interactive column using Java applets by Alex Bogomolny
<http://www.cut-the-knot.com/ctk/March2001.html>

IMAGES

An Image From the Collatz Problem

By Andrew Shapira
<http://www.cs.rpi.edu/~shapiraa/collatz.html>
The Complexity of the Collatz problem
<http://www.geocities.com/CapeCanaveral/Lab/4430/collatz.html>

LOGICIELS - SOFTWARES

DEMO: Collatz function

Selmer Bringsjord
<http://www.rpi.edu/~brings/locker/collatz.lisp>

JAVA

A two-register abacus applet
<http://cs.stmarys.ca/~dawson/Abacus.html>

DONNÉES - DATAS

The Collatz Problem (3x+1)

Evans A Criswell
<http://home.hiwaay.net/~criswell/math/collatz.html>

LIVRES - BOOKS

Unsolved Problems in Number Theory (Problem Books in Mathematics, Vol 1)

by Richard K. Guy
<http://www.amazon.com/exec/obidos/ISBN%3D0387942890/ericstreasuretroA/002-6234887-4574852>

DOCUMENTS - PAPERS

Collatz Problem
<http://www.cs.unb.ca/~alopez-o/math-faq/node61.html>
Ken Monks's Faculty-Student Research Program Information
<http://academic.uofs.edu/faculty/monks/fsrp.html>
The 3x+1 Problem

Research Directed by Gary T. Leavens
<http://www.cs.iastate.edu/~leavens/main.html#3x+1>
A Distributed Search Program for the 3x+1 problem.

Gary T. Leavens

Full text Postscript Adobe PDF

This report describes the design of a distributed program that searched for peaks in certain measures related to the 3x+1 problem. The searches for peaks in the number of steps taken, the maximum value reached, and the number of steps before the values of the iterates fall below the starting value exhibit a great deal of parallelism, but there is also some small amount of synchronization necessary.
<ftp://ftp.cs.iastate.edu/pub/techreports/TR89-22/TR.ps.Z>
3x + 1 Search Programs

by Gary T. Leavens and Mike Vermeulen
<http://archives.cs.iastate.edu/documents/disk0/00/00/00/12/index.html>
Computer Science Technical Reports
<http://www.cs.iastate.edu/tech-reports/catalog.html>
A heuristic argument.
<http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/>
lagarias
<http://cecm.sfu.ca/organics/papers/lagarias/paper/html/anhtml/node1-an2.sec>
The 3n+1 problem.

Ioannis Galidakis
<http://users.forthnet.gr/ath/jgal/math/problem.html>
3n+1.pub.ps D. Schleicher
<http://pckoenig1.mathematik.tu-muenchen.de/~dierk/3n+1.pub.ps>
03: Mathematical logic and foundations

by Dave Rusin Math Atlas
<http://www.math.niu.edu/~rusin/papers/known-math/index/03-XX.html>
The 3n+1 Collatz Problem and Functional Equations

Berg, Lothar

This paper reports on some functional equations, which arise in connection with the famous 3n+1 Collatz problem. In particular, it reports on two analytic versions of the corresponding Collatz conjecture, which are contained in [1]
<ftp://ftp.math.uni-rostock.de/pub/romako/heft48/berg2.ps.Z>
Chains in Collatz's Tree

Stefan Andrei, Manfred Kudlek and Radu Niculescu Stefan B-217 May 28, 1999
<http://medoc.informatik.uni-hamburg.de/Dienst/UI/2.0/Describe/ncstrl.uhamburg_cs%2FB-217>
A binomial representation of the 3x+1 problem

found by Maurice Margenstern and Yuri Matiyasevich Published in Acta Arithmetica, XCI.4, 1999, 367-378
<http://www.informatik.uni-stuttgart.de/ifi/ti/personen/Matiyasevich/Journal/jcontord.htm>
A possible solution to the 3x + 1 problem

Peter Schorer and Michael O'Neill September 5, 2001
<http://www.occampress.com/final2.pdf>
The Arithmetic Properties of Binomial Coefficients

Andrew Granville 1996
<http://www.cecm.sfu.ca/cgi-bin/organics/doc_vault/name=paper+access_path=papers/granville/vault>
Cyclic Structure of Dynamical Systems Associated with $3x+d$ Extensions of Collatz Problem.

Edouard Belaga,Maurice Mignotte May 2000

Reflecting on the 3x+1 Mystery. Outline of a Scenario. Effective Polynomial Upper Bounds to Perigees and Numbers of $(3x+d)-$Cycles of a Given Oddlength.
<http://www-irma.u-strasbg.fr/irma/publications/2000/00018.shtml>
Survey on the Generalized 3x+1 Problem

Keith Matthews survey (pdf), programs, results ...

On Shanks' algorithm for computing the continued fraction of log_b a Terence Jackson and Keith Matthews
<http://www.numbertheory.org/ntw/N4.html#3x+1>
The 3x+1 Problem and Directed Graphs.

Paul J Andaloro Kent State University
<http://www.math.grin.edu/~chamberl/conference/papers/anda.ps>
Applied number theory, recurring sequences, the 3x+1 problem.

J.L. (John) Simons Professor of Information Systems Groningen

For an overview of the recent developments, see an intended 2009 Mathfest presentation /staff/j.l.simons/recdevslides.pdf [PDF] .

a proof for the non-existence of 2-cycles, a simple proof for 2-cycles based on an induction argument from 1-cycles.
<http://www.rug.nl/staff/j.l.simons/research>

RÉSUMÉS - ABSTRACTS

The relation between collatz conjecture and primes

Murad A. AlDamen
<http://atlas-conferences.com/c/a/f/t/16.htm>
About the Collatz conjecture

Stefan Andrei, Cristian Masalagiu
<http://link.springer-ny.com/link/service/journals/00236/bibs/8035002/80350167.htm>

JOURNAUX - LETTERS

Computers & Mathematics with Applications Elsevier

An International Journal
<http://www.elsevier.com:80/inca/publications/store/3/0/1/>

TUTORIELS - TUTORIALS - TUTORS

The 3x + 1 Problem and its Generalizations

Jeffrey C. Lagarias
<http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/paper.html>

ARTICLES

PC World Malta Article 8 - The Collatz Problem
<http://www.bms.com.mt/archive/iss22/num08.htm>

CONFÉRENCES - MEETINGS

International Conference on the Collatz Problem and Related Topics

August 5-6, 1999 Katholische UniversitÃ¤t EichstÃ¤tt, GERMANY
<http://www.math.grinnell.edu/~chamberl/conf.html>

HISTORIQUES - HISTORY

Translation of the Collatz letter (to Professor Mays)

by Marion Meudt and John Read
<http://www.cecm.sfu.ca/organics/papers/lagarias/paper/goodies/ubersetzung/html/ubersetzung.html>

ARTS

The Music of Hailstones

Mike Keith

... To bring this into the range of a musical melody, we pass each number through the following function: f(n) = [ (10/3) log10(n) ] ... These numbers are interpreted as notes in the 7-tone major scale, with 0=root, 1=next note, etc.
<http://user.aol.com/s6sj7gt/hailmus.htm>

RÉFÉRENCES - BIBLIOGRAPHIES

Collection of References
<http://felix.unife.it/Root/d-Mathematics/d-Number-theory/b-3x+1>
Collatz (3x+1) Problem References
<http://ug.cs.dal.ca/~campbell/collrefs.html>
The 3x+1 Problem: An Annotated Bibliography, II (2001-)

Jeffrey C. Lagarias

arXiv:math/0608208v3 This paper is an annotated bibliography of work done on the 3x+1 problem published from 2001 onward. This is a sequel to an annotated bibliography on the 3x+1 problem covering 1963-2000 >. At present the 3x+1 Conjecture remains unsolved.

The 3x+1 problem: An annotated bibliography (1963--2000) arXiv:math/0309224v9
<http://arxiv.org/abs/math/0608208>

QUESTIONS - FAQ

Frequently Asked Questions in Mathematics
<http://www.cs.unb.ca/~alopez-o/math-faq/math-faq.html>
sci.math FAQ: Unsolved Problems
<http://www.faqs.org/faqs/sci-math-faq/unsolvedproblems/>

GROUPES DE DISCUSSION - NEWS

Collatz problem; 3x+1 problem; total stopping time function

by David Bernier
<http://forum.swarthmore.edu/epigone/sci.math/zandbape>
Hailstone Anyone?

Danny Calegari
< http://www.math.niu.edu/~rusin/papers/known-math/96/halting>
Collatz "proof"

Dave Rusin
<http://www.math.niu.edu/~rusin/known-math/98/collatz_mine>
Connection between Collatz and Catalan conjectures.

Dave Rusin

Elementary number theory
<http://www.math.niu.edu/~rusin/known-math/98/collatz_catalan>

LIENS - LINKS

Collatz (3x+1) Problem WWW Links
<http://ug.cs.dal.ca/~campbell/colllink.html>
StÃ©fane Fermigier's Elliptic Curves Page.

This page is a collection of links on research articles on elliptic curves and related topics (applications, modular forms, FLT).
<http://www.math.jussieu.fr/~fermigie/elliptic.html.en>
AltaVista 3x+1 Problem
<http://www.altavista.com/cgi-bin/query?pg=q&what=web&fmt=.&q=%223x+1+Problem%22>
Collatz_Problem - (300 Sites)
<http://www.geometry.net/Theorems_and_Conjectures/Collatz_Problem.htm>

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