On sidon sequences of farey sequences, square roots and reciprocals
Gergő Surányi · Mathematica Slovaca · 2020
Abstract In this paper, I will construct three families of Sidon sequences of certain subsets of ℝ, in particular I will study Farey sequences, square roots, and reciprocals. It will be shown that Sidon sequences over them have cardinality of between c 1 N 3 / 4 log N $\begin{array}{} \displaystyle c_1\frac{N^{3/4}} {\log{N}} \end{array}$ and c 2 N 3/4, c 3 N, and c 4 N log log N log N . $\begin{array}{} \displaystyle c_4 \frac{N\log{\log{N}}}{\log{N}}. \end{array}$