Maximal density and the kappa values for the families $\{a,a+1,2a+1,n\}$ and $\{a,a+1,2a+1,3a+1,n\}$

Ram Krishna Pandey, Neha Rai

Let $M$ be a set of positive integers. We study the maximal density $\mu (M)$ of the sets of nonnegative integers $S$ whose elements do not differ by an element in $M$. In 1973, Canto…