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

Paula Neeley, Daniel Taylor-Rodriguez, J. J. P. Veerman, Thomas Roth

Published 2018-06-10Version 1

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.