Infinite Sidon sequences

Javier Cilleruelo

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arXiv · 1209.0326

Infinite Sidon sequences

Javier Cilleruelo

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Abstract

We present a new method to obtain infinite Sidon sequences, based on the discrete logarithm. We construct an infinite Sidon sequence A, with A(x)= x^{\sqrt 2-1+o(1)}. Ruzsa proved the existence of a Sidon sequence with similar counting function but his proof was not constructive. Our method generalizes to B_h sequences: For all h\ge 3, there is a B_h sequence A such that A(x)=x^{\sqrt{(h-1)^2+1}-(h-1)+o(1)}.

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Javier Cilleruelo. 2013-05-15. Infinite Sidon sequences. https://arxiv.org/abs/1209.0326

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