Publicacions Matemàtiques

Dense Infinite $B_h$ Sequences

Javier Cilleruelo and Rafael Tesoro

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For $h=3$ and $h=4$ we prove the existence of infinite $B_h$ sequences $\mathcal{B}$ with counting function

$$\mathcal{B}(x)= x^{\sqrt{(h-1)^2+1}-(h-1) + o(1)}.$$

This result extends a construction of I. Ruzsa for $B_2$ sequences.

Article information

Publ. Mat., Volume 59, Number 1 (2015), 55-73.

First available in Project Euclid: 21 January 2015

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11B83: Special sequences and polynomials

$B_h$ sequences Sidon sequences probabilistic method


Cilleruelo, Javier; Tesoro, Rafael. Dense Infinite $B_h$ Sequences. Publ. Mat. 59 (2015), no. 1, 55--73.

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