NÚMEROS DE BALL GENERALIZADOS

Abstract

A study on Ball's magic numbers in base 10 and some properties are considered in Costa [4] and Costa and Mesquita [5]. In the first the authors proved that every Ball's magic numbers are multiple of 99, while in [4] a relationship between the quantity of Ball's magic numbers and the Fibonacci sequence is showned. In this work we extend the concept of Ball's magic number for any base b> 2,  generalized Ball's magic number. We show some properties and prove that, for any base b>2, the generalized Ball's magic number is a multiple of (aa)_b, where a = b-1. Furthermore, following Webster [10] and Costa [4], we present a relationship between the generalized Ball's magic numbers and the Fibonacci sequence.