Question 47
We say a set $\{a_1, \dots, a_n\}$ of real numbers is *interesting* if for all $1 \lt i \lt n$ we have $0 \lt a_{i+1} - a_i \lt a_i - a_{i-1}$. For each positive integer $m$ find the smallest positive integer $k$ such that there is an interesting set $A$ with $k$ elements such that $1$ can be written in at least $m$ different ways as the difference of two elements of $A$.