Dense infinite $B_h$ sequences

Javier Cilleruelo, Rafael Tesoro

For $h=3$ and $h=4$ we prove the existence of infinite $B_h$ sequences $\B$ with counting function $$\mathcal{B}(x)=x^{\sqrt{(h-1{)}^2+1}-(h-1)+o(1)}.$$ This result extends a cons…