About a new family of sequences

TL;DR

This paper introduces a novel family of sequences derived from a new class of functions over natural numbers, revealing self-similarity properties in some of these sequences.

Contribution

It defines a new type of functions and sequences over natural numbers, and explores their self-similarity features, which is a novel approach in sequence analysis.

Findings

Some sequences exhibit self-similarity

New functions over natural numbers are introduced

Sequences have potential applications in recursive structures

Abstract

First we define a new kind of function over $\mathbb{N}$. For each $i\in\mathbb{N}$ we have an associated function, which will be called $S_i$ . Then we define a new kind of sequence, to be made from the functions $S_i$ . Finally, we will see that some of these sequences has a self-similarity feature.