About: Kaprekar's routine

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In number theory, Kaprekar's routine is an iterative algorithm that, with each iteration, takes a natural number in a given number base, creates two new numbers by sorting the digits of its number by descending and ascending order, and subtracts the second from the first to yield the natural number for the next iteration. It is named after its inventor, the Indian mathematician D. R. Kaprekar.

Attributes	Values
rdfs:label	Algorithme de Kaprekar (fr) Kaprekar's routine (en)
rdfs:comment	En mathématiques, l’algorithme de Kaprekar est un algorithme qui transforme un nombre entier en un autre, de façon répétitive jusqu'à arriver à un cycle. Il fut découvert en 1949 par le mathématicien indien Dattatreya Ramachandra Kaprekar pour les nombres de quatre chiffres, mais il peut être généralisé à tous les nombres. (fr) In number theory, Kaprekar's routine is an iterative algorithm that, with each iteration, takes a natural number in a given number base, creates two new numbers by sorting the digits of its number by descending and ascending order, and subtracts the second from the first to yield the natural number for the next iteration. It is named after its inventor, the Indian mathematician D. R. Kaprekar. (en)
foaf:depiction
dcterms:subject	Base-dependent integer sequences Arithmetic dynamics Sorting algorithms
Wikipage page ID	1497098 (xsd:integer)
Wikipage revision ID	1123302513 (xsd:integer)
Link from a Wikipage to another Wikipage	Python (programming language) Base-10 Base 10 Base 16 Brady Haran Decimal Perfect digital invariant Cycle detection University of Nottingham Iterative Perfect digit-to-digit invariant Function (mathematics) Base-dependent integer sequences Mathematician Arithmetic dynamics Sorting algorithms Dudeney number 6174 (number) 495 (number) D. R. Kaprekar Factorion Fixed point (mathematics) Base 2 Number theory Base-16 Digit sum Happy number Kaprekar's routine Kaprekar number Arithmetic dynamics Sorting algorithm India Natural number Meertens number Narcissistic number Sum-product number Repdigit Base-12 Base-2 Base-4 Base-6 Base-8 Base 12 Base 3 Base 4 Base 5 Base 6 Base 8 Base 9 Number base Zero (number)
Link from a Wikipage to an external page	https://www.youtube.com/watch%3Fv=d8TRcZklX_Q http://www.numberphile.com/videos/6174.html%7Cwork=Numberphile%7Cpublisher= https://web.archive.org/web/20170823224728/http:/www.numberphile.com/videos/6174.html%7Carchive-date=2017-08-23%7Curl-status=dead https://arxiv.org/abs/1710.06308 http://www.panix.com/~baldwin/kaprekar.pl
sameAs	Kaprekar's routine Kaprekar's routine Kaprekar's routine Kaprekar's routine Kaprekar's routine
dbp:wikiPageUsesTemplate	dbt:Cite_journal dbt:Cite_web dbt:Commons_category dbt:Refbegin dbt:Refend dbt:Reflist dbt:Sfn dbt:Short_description dbt:Math_proof dbt:Classes_of_natural_numbers
thumbnail	wiki-commons:Special:FilePath/KaprekarRoutineFlowGraph6174.svg?width=300
title	Proof (en)
drop	hidden (en)
has abstract	In number theory, Kaprekar's routine is an iterative algorithm that, with each iteration, takes a natural number in a given number base, creates two new numbers by sorting the digits of its number by descending and ascending order, and subtracts the second from the first to yield the natural number for the next iteration. It is named after its inventor, the Indian mathematician D. R. Kaprekar. Kaprekar showed that in the case of four-digit numbers in base 10, if the initial number has at least two distinct digits, after seven iterations this process always yields the number 6174, which is now known as Kaprekar's constant. (en) En mathématiques, l’algorithme de Kaprekar est un algorithme qui transforme un nombre entier en un autre, de façon répétitive jusqu'à arriver à un cycle. Il fut découvert en 1949 par le mathématicien indien Dattatreya Ramachandra Kaprekar pour les nombres de quatre chiffres, mais il peut être généralisé à tous les nombres. (fr)
prov:wasDerivedFrom	wikipedia-en:Kaprekar's_routine?oldid=1123302513&ns=0
page length (characters) of wiki page	24048 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Kaprekar's_routine
is Link from a Wikipage to another Wikipage of	Perfect digital invariant 100,000,000 Perfect digit-to-digit invariant Dudeney number 6174 (number) 495 (number) D. R. Kaprekar Factorion

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