-sequences from -sequences

Author:
Bernt Lindström

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

MSC (2000):
Primary 11B75, 11P99

Published electronically:
September 9, 1999

MathSciNet review:
1636907

Full-text PDF Free Access

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 .*

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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:
http://dx.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