https://github.com/centic9/multiplicativedigitalroot

This project plays with the mathematical topics of "Multiplicative digital roots" and "Multiplicative Persistence"
https://github.com/centic9/multiplicativedigitalroot

bigintegers digits mathematics multiplication

Last synced: 14 days ago
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This project plays with the mathematical topics of "Multiplicative digital roots" and "Multiplicative Persistence"

• Host: GitHub
• URL: https://github.com/centic9/multiplicativedigitalroot
• Owner: centic9
• License: bsd-2-clause
• Created: 2019-10-03T16:06:48.000Z (about 5 years ago)
• Default Branch: master
• Last Pushed: 2023-01-14T23:07:42.000Z (almost 2 years ago)
• Last Synced: 2024-10-30T04:57:40.550Z (2 months ago)
• Topics: bigintegers, digits, mathematics, multiplication
• Language: Java
• Size: 192 KB
• Stars: 1
• Watchers: 4
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

        
[![Build Status](https://travis-ci.org/centic9/MultiplicativeDigitalRoot.svg)](https://travis-ci.org/centic9/MultiplicativeDigitalRoot) 

[![Gradle Status](https://gradleupdate.appspot.com/centic9/MultiplicativeDigitalRoot/status.svg?branch=master)](https://gradleupdate.appspot.com/centic9/MultiplicativeDigitalRoot/status)

This project plays with the mathematical topics of "Multiplicative digital roots" and 

"Multiplicative Persistence", see https://en.wikipedia.org/wiki/Multiplicative_digital_root and 

https://en.wikipedia.org/wiki/Persistence_of_a_number for more information.

It determines the smallest number for each multiplicative persistence using Java and BigInteger or byte-arrays, 

exploring limits of handling large numbers with BigIntegers and comparing performance to other approaches.

## Theory

There is a conjecture that there is no multiplicative persistence of a number higher than 11

See https://oeis.org/A007954 and https://oeis.org/A003001 for related mathematical series

More information on this topic:

* https://de.wikipedia.org/wiki/Querprodukt (German)

* https://www.spektrum.de/kolumne/behaglich-beharrliche-berechnungen/1643996 (German)

* https://arxiv.org/abs/1307.1188

* http://mathworld.wolfram.com/MultiplicativePersistence.html

* http://neilsloane.com/doc/persistence.html

* http://web.archive.org/web/20050214141815/http://www.wschnei.de/digit-related-numbers/persistence.html

* https://www.youtube.com/watch?v=Wim9WJeDTHQ

* http://www41.homepage.villanova.edu/robert.styer/MultiplicativePersistence/PersistenceStephPerezJournalArtAug2013.pdf

* http://markdiamond.com.au/download/joous-3-1-1.pdf

* https://www.tandfonline.com/doi/abs/10.1080/10586458.2014.910849

* https://www.linkedin.com/pulse/calculating-multiplicative-persistence-efficiently-cecil-westerhof/?trk=public_profile_article_view

* https://opensourc.es/blog/persistence/

## Code

This project currently implements two ways of computing the multiplicative persistence of 

numbers.

The first version at `MultiplicativeDigitalRoot` uses Strings and BigIntegers to handle large numbers, but this is

obviously rather inefficient and limits the number of checks that can be performed.

The second version at `MultiplicativeDigitalRootByteArray` represents the digits of the number in a byte-array which

allows to perform some of the operations much quicker. It also optimizes incrementing the number a lot to check

much less numbers and skip large sections of numbers that are not relevant anyway.

The third version at `MultiplicativeDigitalRootClass` is similar to the previous one but 

extracts code into a class `ByteArrayInteger` which encapsulates the handling of 

## Change it

### Grab it

    git clone https://github.com/centic9/MultiplicativeDigitalRoot.git

### Build it and run tests

    cd MultiplicativeDigitalRoot

    ./gradlew check jacocoTestReport

#### Licensing

* MultiplicativeDigitalRoot is licensed under the [BSD 2-Clause License].

[BSD 2-Clause License]: https://www.opensource.org/licenses/bsd-license.php