Jump to ContentJump to Main Navigation
Show Summary Details
More options …



Mathematical Citation Quotient (MCQ) 2016: 0.40

See all formats and pricing
More options …

Numbers with Integer Complexity Close to the Lower Bound

Harry Altman / Joshua Zelinsky
Published Online: 2012-11-30 | DOI: https://doi.org/10.1515/integers-2012-0031


Define to be the complexity of n, the smallest number of ones needed to write n using an arbitrary combination of addition and multiplication. John Selfridge showed that for all n. Define the defect of n, denoted by , to be ; in this paper we present a method for classifying all n with for a given r. From this, we derive several consequences. We prove that for with m and k not both zero, and present a method that can, with more computation, potentially prove the same for larger m. Furthermore, defining to be the number of n with and , we prove that , allowing us to conclude that the values of can be arbitrarily large.

Keywords: Integer Complexity; Integer Sequence; Arithmetic; Arithmetic Operations

About the article

Received: 2011-06-28

Revised: 2012-06-25

Accepted: 2012-07-24

Published Online: 2012-11-30

Published in Print: 2012-12-01

Citation Information: Integers, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2012-0031.

Export Citation

© 2012 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Harry Altman
Theoretical Computer Science, 2016, Volume 652, Page 64

Comments (0)

Please log in or register to comment.
Log in