Transformations Integer Sequences And Pairing Functions

TL;DR

This paper introduces new methods for generating integer sequences using Cantor diagonalization, including modifications and generalizations, with explicit formulas provided for these new families.

Contribution

It presents novel procedures for creating and generalizing integer sequences based on Cantor diagonalization, expanding the toolkit for sequence construction.

Findings

Explicit formulas for new integer sequence families

Generalized methods for sequence creation

Enhanced understanding of pairing functions

Abstract

We propose several procedures for creating new families of integer sequences based on the method of Cantor diagonalization. Then we modify and generalize this method. The paper includes explicit formulas for most proposed families of integer sequences.