#### Title

An Analysis of the Distribution of Numbers of the Form alpha[superscript x] beta[superscript y]

#### Date of Award

12-2010

#### Document Type

Thesis

#### Degree Name

Master of Science (MS)

#### Department

Mathematics

#### First Advisor

John J. Lattanzio, Ph.D.

#### Second Advisor

Daniel A. Burkett, Ph.D.

#### Third Advisor

John H. Steelman, Ph.D.

#### Abstract

This thesis will provide an analysis of the sequences formed in an interspersion. It is known that interspersions can be generated entirely from two infinite sequences of positive integers. Since these sequences are based on the integer parts of multiples of an irrational number, finding an expression for one is equivalent to finding an expression for the other. We shall see that sums involving the floor of an integer multiple of an irrational number 0 can be evaluated by first expressing the indices of a summation in the numeration system based on the denominators of the convergents of 0. We shall then turn our attention towards counting the number of times a particular element appears in some sequence G. It will be shown that a minimum of two repetition lengths occur.

#### Recommended Citation

Hewitt, Jared, "An Analysis of the Distribution of Numbers of the Form alpha[superscript x] beta[superscript y]" (2010). *Theses and Dissertations (All)*. 1010.

https://knowledge.library.iup.edu/etd/1010