Behavior of the numbers in the Beta expansion.

Abstract

In this report, we show the result of numerical calculation about the beta-expansion of real number a. As a result, we found that the ratio of each integer would change self-similarly depending on a change of β regardless of number a. In the case of 2<β<3, the values of β which have the same rario between 1 and 2, are given by the solutions of equations β－2=0，（β－2）β－2=0，（（β－2）β－2）β－2=0，….