Journal of Integer Sequences, Vol. 12 (2009), Article 09.1.1

Some Postage Stamp 2-Bases

John P. Robinson
Coordinated Laboratory for Computational Genomics
University of Iowa
Iowa City, IA 52242


A set of k integers is a 2-basis if every positive integer up to n can be expressed as the sum of no more than 2 values from the set; an extremal 2-basis is one for which n is as large as possible. A new algorithm extends the lower bound of Mossige for symmetric bases. An assumed modulo structure is combined with local search. These 2-bases match all known extremal values for k from 11 to 20. Bases out to k = 82 are given.

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(Concerned with sequence A001212.)

Received September 9 2008; revised version received November 19 2008. Published in Journal of Integer Sequences, December 14 2008.

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