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On Weakly Complete Sequences Formed by the Greedy Algorithm

Michael P. Knapp / Michael D. Paul
Published Online: 2012-08-01 | DOI: https://doi.org/10.1515/integers-2011-0118


In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any define to be the smallest integer greater than which cannot be written as a sum of (distinct) previous terms of the sequence. For various parametrized choices of the initial terms, we determine precisely the terms of the sequences obtained by this method. We also conjecture that for all choices of the initial terms, even in a more general setting, the terms of sequences defined in this manner have interesting patterns.

Keywords: Weakly Complete Sequences; Greedy Algorithm; Patterns in Sequences

About the article

Received: 2011-05-03

Accepted: 2011-12-09

Published Online: 2012-08-01

Published in Print: 2012-08-01

Citation Information: Integers, Volume 12, Issue 4, Pages 473–490, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2011-0118.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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