# Variants of Base 3 over 2

## TL;DR

This paper explores two distinct base 3/2 number systems that uniquely represent integers finitely and examines their connection to 3-free sequences, providing insights into alternative number representations.

## Contribution

It introduces and compares two different base 3/2 systems that allow finite integer representations and links them to 3-free sequences, expanding understanding of non-standard number systems.

## Key findings

- Both systems provide finite representations for integers.
- The systems are connected through a specific mathematical relationship.
- A link between these systems and 3-free sequences is established.

## Abstract

We discuss two different systems of number representations that both can be called 'base 3/2'. We explain how they are connected. Unlike classical fractional extension, these two systems provide a finite representation for integers. We also discuss a connection between these systems and 3-free sequences.