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Kaprekar's routine Algorithme de Kaprekar
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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. 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.
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Proof
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hidden
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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. 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 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.
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