Curious Properties of Iterative Sequences
Shoei Takahashi, Unchone Lee, Hikaru Manabe, Aoi Murakami, Daisuke, Minematsu, Kou Omori, Ryohei Miyadera
TL;DR
This paper explores various intriguing properties of iterative sequences, including new variants of Kaprekar's routine, by analyzing fixed functions and their behaviors in different digit-based processes.
Contribution
It introduces novel variants of Kaprekar's routine and investigates properties of iterative sequences involving fixed functions and digit-based processes.
Findings
New variants of Kaprekar's routine are proposed.
Iterative sequences exhibit interesting convergence properties.
Digit factorial and power processes reveal unique sequence behaviors.
Abstract
In this study, several interesting iterative sequences were investigated. First, we define the iterative sequences. We fix function f(n). An iterative sequence starts with a natural number n, and calculates the sequence f(n),f(f(n)), ...f(f(f(f(n)))),... We then search for interesting features in this sequence. We study Kaprekar's routine, the digit factorial process, and the digit power process. The authors presented new variants of Kaprekar's routine.
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Taxonomy
TopicsVaried Academic Research Topics