-sequences from -sequences

Author:
Bernt Lindström

Journal:
Proc. Amer. Math. Soc. **128** (2000), 657-659

MSC (2000):
Primary 11B75, 11P99

DOI:
https://doi.org/10.1090/S0002-9939-99-05122-9

Published electronically:
September 9, 1999

MathSciNet review:
1636907

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Abstract | References | Similar Articles | Additional Information

Abstract: A sequence of positive integers is called a -sequence if every integer has at most representations with all in and . A -sequence is also called a -sequence or Sidon sequence. The main result is the following

**Theorem.** *Let be a -sequence and for an integer . Then there is a -sequence of size , where .*

**Corollary.** *Let . The interval then contains a -sequence of size , when .*

**[1]**A. Balog, Review of [2]. MR**90d:11022****[2]**D. Hajela,*Some remarks on -sequences*, J. Number Theory**29**(1988), 311-323. MR**90d:11022****[3]**H. Halberstam and K. F. Roth, ``Sequences'', Oxford, 1966. MR**35:1565****[4]**X.-D. Jia,*-sequences with large upper density*, J. Number Theory**56**(1996), 298-308. MR**96k:11009****[5]**T. Kløve,*Constructions of -sequences*, Acta Arith.**58**(1991), 65-78. MR**92f:11033****[6]**M. N. Kolountzakis,*The density of -sequences and the minimum of dense cosine sums*, J. Number Theory**56**(1996), 4-11. MR**96k:11026**

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Additional Information

**Bernt Lindström**

Affiliation:
Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden

Email:
bernt@math.kth.se

DOI:
https://doi.org/10.1090/S0002-9939-99-05122-9

Keywords:
$B_h$-sequence,
Sidon sequence

Received by editor(s):
April 17, 1998

Published electronically:
September 9, 1999

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 1999
American Mathematical Society