╨╧рб▒с>■ "$■ ! ье┴Y ┐0bjbjєWєW )С=С=0 ]жжжжжжж╓╓╓╓╓т╓Q╢········$Ї√r<ж·····<nжж···nnn·^ж·ж·║╚жжжж·nиnжж·ю ╡bу9}┬╓╓XInvestigations into the Kaprekar Process
Abstract
Robert W. Ellis and Jason R. Lewis
D.R. Kaprekar discovered an interesting phenomenon that occurs when one takes a four-digit number, such that all four digits are not equal, and computes the difference between its decreasing and increasing rearrangements. He found that within seven iterations of this process you will always reach the number 6174, and this process became known as the Kaprekar Process. In this paper we decided to investigate the results of the application of the Kaprekar Process to numbers of various digit lengths. This investigation includes new information about the Kaprekar Process, such as a statistical analysis of the Kaprekar Process on four-digit and five-digit numbers, and a description of the relationships between different four-digit numbers after the application of the Kaprekar Process. We also provide a summary of the results of the Kaprekar Process when applied to various digit lengths, and a look at the palindromic sequences which present themselves in this investigation.
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