Problem 1477. Champernowne Constant

Created by G K

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>The</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Champernowne_constant\"><w:r><w:t>Champernowne constant</w:t></w:r></w:hyperlink><w:r><w:t> is a real number whose digits in decimal representation come from the concatenation of all consecutive positive integers starting from 1.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>That is</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 0.1234567891011121314151617181920...]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This constant is of interest because it can be understood to contain an encoding of any past, present or future information, because any given sequence of numbers can be shown to exist somewhere in the champernowne representation.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Return the nth digit of the champernowne constant. The function takes an array of position values and returns an array of digits corresponding to those positions.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Examples:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ [1 2 3 4 5] returns [1 2 3 4 5]\n\n [10 11 12 13 14 15] returns [1 0 1 1 1 2]\n\n [188 289] returns [9 9]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Problem 3) Prev:</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/1472\"><w:r><w:t>1472</w:t></w:r></w:hyperlink><w:r><w:t> Next:</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/1478\"><w:r><w:t>1478</w:t></w:r></w:hyperlink></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>"}]}

The <a href = "http://en.wikipedia.org/wiki/Champernowne_constant">Champernowne constant</a> is a real number whose digits in decimal representation come from the concatenation of all consecutive positive integers starting from 1.That is<pre> 0.1234567891011121314151617181920...</pre>This constant is of interest because it can be understood to contain an encoding of any past, present or future information, because any given sequence of numbers can be shown to exist somewhere in the champernowne representation.Return the nth digit of the champernowne constant. The function takes an array of position values and returns an array of digits corresponding to those positions.Examples:<pre> [1 2 3 4 5] returns [1 2 3 4 5]</pre><pre> [10 11 12 13 14 15] returns [1 0 1 1 1 2]</pre><pre> [188 289] returns [9 9] </pre>Problem 3)
Prev: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1472">1472</a>
Next: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1478">1478</a>

Solve

Solution Stats

139 Solutions
42 Solvers

Last Solution submitted on Oct 09, 2020

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

James on 14 May 2013

Please change the example [188 289] in your problem description to [188 189], as I believe [188 289] should return [9 1], rather than [9 9]. (By the way, great job picking 189 to use for a check. Right at the end of the two-digit numbers.)

Rafael S.T. Vieira on 14 Aug 2020

uint8 is our friend.

Problem Recent Solvers42

Problem Tags

math

Community Treasure Hunt

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

Start Hunting!

Problem 1477. Champernowne Constant

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers42

Suggested Problems

More from this Author10

Problem Tags

Community Treasure Hunt

Problem 1477. Champernowne Constant

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers42

Suggested Problems

More from this Author10

Problem Tags

Community Treasure Hunt

Players