Problem 42673. Longest Collatz Sequence

Created by Jean-Marie Sainthillier

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Inspired by Projet Euler n°14.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The Collatz iterative sequence (See Cody problem n° 2103 and 211) is defined for the set of positive integers:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>n → n/2 (n is even)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>n → 3n + 1 (n is odd)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Using the rule above and starting with 13, we generate the following sequence:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Which starting number, under number given in input, produces the longest chain?</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Be smart because numbers can be big...</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

257 Solutions
82 Solvers

Last Solution submitted on May 26, 2023

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

li haitao on 26 Oct 2018

Please try to solve a harder version "Problem 44448. Project Euler: Problem 14 Longest Collatz sequence"

https://ww2.mathworks.cn/matlabcentral/cody/problems/44448

Solution Comments

Show comments

Problem Recent Solvers82

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 42673. Longest Collatz Sequence

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers82

Suggested Problems

More from this Author43

Problem Tags

Community Treasure Hunt

Problem 42673. Longest Collatz Sequence

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers82

Suggested Problems

More from this Author43

Problem Tags

Community Treasure Hunt

Players