The sum of digits of $n$ and $n^2$

K. G. Hare, S. Laishram, T. Stoll

Let $s_q(n)$ denote the sum of the digits in the $q$-ary expansion of an integer $n$. In 2005, Melfi examined the structure of $n$ such that $s_2(n)=s_2(n^2)$. We extend this stu…