• Corpus ID: 240354446

Algebraic Kaprekar routine architecture II

```@inproceedings{Nuez2021AlgebraicKR,
title={Algebraic Kaprekar routine architecture II},
author={Fernando Nuez},
year={2021}
}```
• F. Nuez
• Published 29 October 2021
• Mathematics, Computer Science
Kaprekar’s routine consists in sorting the digits of a number n in descending order, resulting X. Then, Y is obtained by sorting the digits in ascending order, and these numbers are subtracted n’ = X-Y. When iterating the process with n’ and beyond, Kaprekar (1949) showed that if n has four non-identical digits such iteration leads to 6174. Additionally, if the number n has three digits the routine leads to 495. These numbers are known as Kaprekar constants. In the first part of this paper…
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Tables from this paper

Parametric transformation functions in the Kaprekar routine I
• F. Nuez
• Mathematics, Computer Science
• 2021
This work develops Ki functions that provide the parameters of the transformed number Ki (α) = α’ that are used to study the algebraic architecture of the transformation trees that are developed in the second part of this work.

References

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Kaprekar’s Routine is an iteration process that, with each iteration, sorts the digits of a number in descending and scending orders and uses their difference for the next iteration. In this paper,
The Base Dependent Behavior of Kaprekar's Routine: A Theoretical and Computational Study Revealing New Regularities
Consider the following process: Take any four-digit number which has at least two distinct digits. Then, rearrange the digits of the original number in ascending and descending order, take these two
Terminating cycles for iterated difference values of five digit integers.
The Kaprekar Constant 6174 received attention a short time ago in Martin Gardner's Scientific American Section "Mathematical Games" (see [4]), and more recently in an article by H. Hasse and this
Parametric transformation functions in the Kaprekar routine I
• F. Nuez
• Mathematics, Computer Science
• 2021
This work develops Ki functions that provide the parameters of the transformed number Ki (α) = α’ that are used to study the algebraic architecture of the transformation trees that are developed in the second part of this work.
Searching for Kaprekar's constants: algorithms and results
This work establishes the unique 7-digit and 9-digit Kaprekar constants and shows that there are no 15-, 21-, 27-, or 33-digit Kanrekar's constants.
Maximum distances in the four-digit Kaprekar process
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• 2020
For natural numbers \$x\$ and \$b\$, the classical Kaprekar function is defined as \$K_{b} (x) = D-A\$, where \$D\$ is the rearrangement of the base-\$b\$ digits of \$x\$ in descending order and \$A\$ is
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• 1981
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Another solitaire game
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