Asymptotic Behavior of Iterated Sets of Remainders

Omkar Baraskar, Prashant Gokhale, Sarvagya Jain +1

For a positive integer $n$, let $$S_0(n)=\{1,2,\dots ,\lfloor n/2\rfloor \},S_{j+1}(n)=\{n\mathrm{mod}k:k\in S_j(n)\setminus \{0\}\},$$ and put $s_j(n):=|S_j(n)|$. The sets define…