On the Uniformity of $(3/2{)}^n$ Modulo 1

Abstract

It has been conjectured that the sequence $(3/2{)}^n$ modulo $1$ is uniformly distributed. The distribution of this sequence is signifcant in relation to unsolved problems in number theory including the Collatz conjecture. In this paper, we describe an algorithm to compute $(3/2{)}^n$ modulo $1$ to $n=10^8$. We then statistically analyze its distribution. Our results strongly agree with the hypothesis that $(3/2{)}^n$ modulo 1 is uniformly distributed.

12 pages, 2 figures