Problem 69. Find the peak 3n+1 sequence value

Created by Cody Team

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>A Collatz sequence is the sequence where, for a given number n, the next number in the sequence is either n/2 if the number is even or 3n+1 if the number is odd. See</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/21-return-the-3n-1-sequence-for-n\"><w:r><w:t>Problem 21</w:t></w:r></w:hyperlink><w:r><w:t> for more information.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Let c(n) be the sequence for n, and p(n) be the peak value of that sequence. For a given threshold nmax, find the highest peak value max(p(n)) for all Collatz sequences starting with integers between 1 and nmax.</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

2164 Solutions
1180 Solvers

Last Solution submitted on Sep 21, 2020

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Hariprasad Baburajan on 25 Dec 2018

Nice one

Zoltán Nagy on 26 Apr 2019

Good problem!

Solution Comments

Solution 2644234

1 Comment

1 Comment

Haoyu Dai on 2 Jul 2020

function pmax = peakOfPeaks(nmax)
pmax=1;
tmp=[];
for i=1:nmax
j=i;
tmp=[tmp j];
while j~=1
if mod(j,2)==0
j=j/2;
tmp=[tmp j];
else
j=3*j+1;
tmp=[tmp j];
end
end
if pmax

Solution 1702070

1 Comment

1 Comment

A C on 3 Jan 2019

How would I speed this up?
If I input nmax = 2^60, my program cannot finish.

Solution 1088348

1 Comment

1 Comment

yurenchu on 25 Dec 2016

This solution will fail for nmax = 2; so I had to swap the order of two lines. See Solution 1088355.

Solution 611646

1 Comment

1 Comment

Wycliff Dembe on 20 Sep 2018

i'm totally lost with this!

Solution 329048

1 Comment

1 Comment

Ted on 4 Oct 2013

wrong, corrected in soln 329062

Solution 267104

1 Comment

1 Comment

Evan on 25 Jun 2013

I only feel justified in doing this because the previous best answer was a look-up table. :P

Solution 24293

1 Comment

1 Comment

Peter Wittenberg on 28 Mar 2012

Clever pattern, but still gaming the system. This is not the absolute highest Collatz peak as you go to infinity. Yuval, you should be ashamed of submitting this without apologies.

Solution 13478

4 Comments

4 Comments

Show 1 older comment

Jed F. on 30 Jan 2012

This really doesn't solve the problem it's just gaming the results.

Kevin Holst on 14 Feb 2012

Boo.

Jean-Yves Tinevez on 17 Feb 2012

Ooooooh this is evil.

Peter Wittenberg on 28 Mar 2012

Pathetic

Problem Recent Solvers1180

Problem Tags

3n+1

Problem 69. Find the peak 3n+1 sequence value

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers1180

Suggested Problems

More from this Author95

Problem Tags

Problem 69. Find the peak 3n+1 sequence value

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers1180

Suggested Problems

More from this Author95

Problem Tags

Players