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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Oscillations of bases for the natural numbers
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by Paul Erdős and Melvyn B. Nathanson
Proc. Amer. Math. Soc. 53 (1975), 253-258
DOI: https://doi.org/10.1090/S0002-9939-1975-0384739-8

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.
References
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 53 (1975), 253-258
  • MSC: Primary 10L05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0384739-8
  • MathSciNet review: 0384739