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

124 Solutions
49 Solvers

Last Solution submitted on Aug 08, 2020

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

Problem Recent Solvers49

Problem Tags

collatz number project euler

Problem 42673. Longest Collatz Sequence

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers49

Suggested Problems

More from this Author43

Problem Tags

Problem 42673. Longest Collatz Sequence

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers49

Suggested Problems

More from this Author43

Problem Tags

Players