Some modular $p$-Stanley sequences
Jonathan Tidor · arXiv (Cornell University) · 2015
The $p$-Stanley sequence of a set $A$ is generated by greedily adding subsequent integers that do not create a $p$-term arithmetic progression. For $p>3$ prime, we prove a result analogous to one of Odlyzko and Stanley on 3-Stanley sequences. We find a class of integers $n$ such that the $p$-Stanley sequence generated from $\{0,n\}$ is modular, a subclass of Stanley sequences which grow as $n^{\log_{(p-1)}p}$. Numerical evidence suggests that these are the only $n$ with this property.