Curious Properties of Iterative Sequences

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.