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- Collatz_conjecture abstract "The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called "Half Or Triple Plus One", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said, allegedly, about the Collatz conjecture: "Mathematics is not yet ripe for such problems." He also offered $500 for its solution.In 1972, J.H. Conway proved that a natural generalization of the Collatz problem is algorithmically undecidable.".
- Collatz_conjecture thumbnail CollatzStatistic100million.png?width=300.
- Collatz_conjecture wikiPageExternalLink hailstone.htm.
- Collatz_conjecture wikiPageExternalLink collatz.
- Collatz_conjecture wikiPageExternalLink PPA336,M1.
- Collatz_conjecture wikiPageExternalLink summary?doi=10.1.1.54.483.
- Collatz_conjecture wikiPageExternalLink collatz-sequence.
- Collatz_conjecture wikiPageExternalLink jpvb_collatz.pdf.
- Collatz_conjecture wikiPageExternalLink CollatzPaths.
- Collatz_conjecture wikiPageExternalLink %5B35%5DSidW-3n+1-ActaArith%5B2005%5D.pdf.
- Collatz_conjecture wikiPageExternalLink 458563.pdf.
- Collatz_conjecture wikiPageExternalLink collatz.
- Collatz_conjecture wikiPageExternalLink Collatz061102.pdf.
- Collatz_conjecture wikiPageExternalLink collloopintro_main.htm.
- Collatz_conjecture wikiPageExternalLink blueprint.html.
- Collatz_conjecture wikiPageExternalLink Le-probleme-3n-1-y-a-t-il-des.html.
- Collatz_conjecture wikiPageExternalLink TagColOK.pdf.
- Collatz_conjecture wikiPageExternalLink p-col.pdf.
- Collatz_conjecture wikiPageExternalLink syracuse.elaunira.com.
- Collatz_conjecture wikiPageExternalLink CTZVI.pdf.
- Collatz_conjecture wikiPageExternalLink collatz.doc.
- Collatz_conjecture wikiPageExternalLink a8*BelagaMathInfo06Presentation060920.ppt.
- Collatz_conjecture wikiPageExternalLink 7.html.
- Collatz_conjecture wikiPageExternalLink index.html.
- Collatz_conjecture wikiPageExternalLink 3x+1.html.
- Collatz_conjecture wikiPageExternalLink collatz.php.
- Collatz_conjecture wikiPageExternalLink 3x+1.
- Collatz_conjecture wikiPageID "37895".
- Collatz_conjecture wikiPageRevisionID "603007321".
- Collatz_conjecture author "Jeffrey C. Lagarias".
- Collatz_conjecture hasPhotoCollection Collatz_conjecture.
- Collatz_conjecture id "BhR-iIjhTNM".
- Collatz_conjecture title "Collatz Iterations on the Ulam Spiral grid".
- Collatz_conjecture title "Collatz Problem".
- Collatz_conjecture title "Syracuse problem".
- Collatz_conjecture urlname "CollatzProblem".
- Collatz_conjecture urlname "S/s110330".
- Collatz_conjecture subject Category:Articles_with_inconsistent_citation_formats.
- Collatz_conjecture subject Category:Conjectures.
- Collatz_conjecture subject Category:Number_theory.
- Collatz_conjecture type Abstraction100002137.
- Collatz_conjecture type Cognition100023271.
- Collatz_conjecture type Concept105835747.
- Collatz_conjecture type Conjectures.
- Collatz_conjecture type Content105809192.
- Collatz_conjecture type Hypothesis105888929.
- Collatz_conjecture type Idea105833840.
- Collatz_conjecture type PsychologicalFeature100023100.
- Collatz_conjecture type Speculation105891783.
- Collatz_conjecture comment "The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937.".
- Collatz_conjecture label "Collatz conjecture".
- Collatz_conjecture label "Collatz-Problem".
- Collatz_conjecture label "Congettura di Collatz".
- Collatz_conjecture label "Conjectura de Collatz".
- Collatz_conjecture label "Conjecture de Syracuse".
- Collatz_conjecture label "Conjetura de Collatz".
- Collatz_conjecture label "Problem Collatza".
- Collatz_conjecture label "Vermoeden van Collatz".
- Collatz_conjecture label "Гипотеза Коллатца".
- Collatz_conjecture label "حدسية كولاتز".
- Collatz_conjecture label "コラッツの問題".
- Collatz_conjecture label "考拉兹猜想".
- Collatz_conjecture sameAs Collatz-Problem.
- Collatz_conjecture sameAs Conjetura_de_Collatz.
- Collatz_conjecture sameAs Conjecture_de_Syracuse.
- Collatz_conjecture sameAs Congettura_di_Collatz.
- Collatz_conjecture sameAs コラッツの問題.
- Collatz_conjecture sameAs 콜라츠_추측.
- Collatz_conjecture sameAs Vermoeden_van_Collatz.
- Collatz_conjecture sameAs Problem_Collatza.
- Collatz_conjecture sameAs Conjectura_de_Collatz.
- Collatz_conjecture sameAs m.09g1c.
- Collatz_conjecture sameAs Q837314.
- Collatz_conjecture sameAs Q837314.
- Collatz_conjecture sameAs Collatz_conjecture.
- Collatz_conjecture wasDerivedFrom Collatz_conjecture?oldid=603007321.
- Collatz_conjecture depiction CollatzStatistic100million.png.
- Collatz_conjecture isPrimaryTopicOf Collatz_conjecture.
