Um estudo sobre as 2-sequências.

Abstract

This thesis presents an original contribution to the theory of numerical sequences through the introduction of a new sequence called the 2-sequence. The central purpose of this study is to associate patterns with pre-existing mathematical concepts, aiming not only to validate known results but also to pave the way for new explorations and discoveries. In analyzing theorems and corollaries, we highlight the use of fundamental mathematical tools, such as the least common multiple, greatest common divisor, numerical and periodic sequences, as well as the period of a sequence. Our goal is not only to present and define the appropriate conceptualization of each tool but also to provide numerical context for a better understanding by the reader. The demonstrations provided not only validate previously known results but also indicate potential opportunities for improvement and further exploration. The 2-sequences, being an initial starting point, prove to be conducive to future explorations involving more advanced mathematical concepts.