# Ultra-recursive sequences

## TL;DR

This paper introduces ultra-recursive sequences, a novel class of self-referential sequences where each term depends on neighboring terms and their properties, expanding the understanding of recursive sequence behaviors.

## Contribution

It defines and explores a new type of sequences with self-referential and bidirectional recursive properties, which had not been studied before.

## Key findings

- Sequences can be generated with terms depending on previous or next elements.
- Ultra-recursive sequences exhibit unique self-referential properties.
- Potential applications in modeling complex recursive systems.

## Abstract

We study a new type of sequences whose elements are defined in terms of the position, sign and magnitude of another element of the sequence. The name ultra-recursive comes from the fact that these sequences possess terms that are generated adding either the previous (as in traditional recurrences formulas) or the next terms. They are also self-referential because the rules to generate every member alludes to some value of the sequence.