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On the Distribution ofB3-Sequences

✍ Scribed by Martin Helm

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 297 KB
Volume: 58
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0069

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✦ Synopsis

An infinite set of natural numbers is called a B 3 -sequence if all sums a 1 +a 2 +a 3 with a j # A and a 1 a 2 a 3 are distinct. Let A(n) be the number of positive elements n in A. P. Erdo s conjectures that every B 3 -sequence A satisfies lim inf n Ä A(n) n &1Â3 =0. In this paper we prove that no sequence satisfying A(n)t:n 1Â3 can be a B 3 -sequence. We also give other necessary conditions for a B 3 -sequence.

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