• 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… 
1 Citations
Parametric transformation functions in the Kaprekar routine I
  • F. Nuez
  • Mathematics, Computer Science
  • 2021
TLDR
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

SHOWING 1-10 OF 10 REFERENCES
On 2-digit and 3-digit Kaprekar's Routine
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
On 2-adic Kaprekar constants and 2-digit Kaprekar distances
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
TLDR
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
TLDR
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
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
The determination of all decadic
  • integers. Journal für die reine und angewandte Mathematik
  • 1981
The determination of all decadic Kaprekar constants
  • Fibonacci Quarterly
  • 1981
Another solitaire game
  • Scripta Mathematica
  • 1949