Some Interesting Properties of Numbers Bases Three Through Ten

Author

Ima Lee Heier, Fort Hays Kansas State College

Department

Math

Degree Name

Master of Science (MS)

Abstract

The primary object of this study was to find n-cycles (n the number of integers in a cycle) of integers in bases three through ten using the function G(A )= [Sigma R/i = 1a 2/I; see manuscript for exact equation] with A = [Sigma R/I =1a/i (IB) R-1; see manuscript for exact equation] as the variable in each base and the ai as digits of A. N-cycles were found for every base from three to ten through the use of an IBM 1401 computer and a Fortran IV program. Since only integers in base 10 of two digits or less were used for the research, the results of the research were justified mathematically by a Convergence Theorem. This theorem shows that an integer in any base converges under successive applications of the operating function G to a number of two digits or less.

Keywords

Integer programming, Mathematics--Formulae, Integral theorems, Numbers--Algebraic, Comparison, Graphs

Advisor

Dr. Wilmont Toalson

Date of Award

Summer 1968

Document Type

Thesis - campus only access

DOI

10.58809/IXCP1292

Recommended Citation

Heier, Ima Lee, "Some Interesting Properties of Numbers Bases Three Through Ten" (1968). Master's Theses. 1156.
DOI: 10.58809/IXCP1292
Available at: https://scholars.fhsu.edu/theses/1156

Rights

© The Author(s)

Comments

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