# "Choix de Bruxelles": A New Operation on Positive Integers

## TL;DR

The paper introduces the 'Choix de Bruxelles' operation on positive integers, exploring its properties and iterative behavior, where numbers are transformed by halving or doubling substrings of their decimal representations.

## Contribution

It defines a novel operation on integers and analyzes its properties and iterative dynamics, which has not been studied before.

## Key findings

- Characterization of possible transformations of integers
- Analysis of the iterative behavior of the operation
- Identification of fixed points and cycles

## Abstract

The "Choix de Bruxelles" operation replaces a positive integer n by any of the numbers that can be obtained by halving or doubling a substring of the decimal representation of n. For example, 16 can become any of 16, 26, 13, 112, 8, or 32. We investigate the properties of this interesting operation and its iterates.