Abstract
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.
Citation
Javier Cilleruelo. Rafael Tesoro. "Dense Infinite $B_h$ Sequences." Publ. Mat. 59 (1) 55 - 73, 2015.
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