Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Oscillations of bases for the natural numbers


Authors: Paul Erdős and Melvyn B. Nathanson
Journal: Proc. Amer. Math. Soc. 53 (1975), 253-258
MSC: Primary 10L05
MathSciNet review: 0384739
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Abstract: Let $ A$ be a set of positive integers. Then $ A$ is a basis if every sufficiently large integer $ n$ can be written in the form $ n = {a_i} + {a_j}$ with $ {a_i},\;{a_j}\epsilon A$. Otherwise, $ A$ is a nonbasis. In this paper we construct sets which oscillate from basis to nonbasis to basis or from nonbasis to basis to nonbasis under finite perturbations of the sets.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0384739-8
Keywords: Minimal basis, maximal nonbasis, sumsets of integers, oscillations of bases, additive number theory
Article copyright: © Copyright 1975 American Mathematical Society