Consider the sequence $x_n = 2^n-n$, $n = 0,1 ,2 ,...$. Find all integers $m \ge 0$ such that $s_m = x_0 + x_1 + x_2 + ... + x_m$ is a power of $2$.
Source: 2011 Saudi Arabia Pre-TST February 2.2
Tags: power of 2, Sum, number theory
Consider the sequence $x_n = 2^n-n$, $n = 0,1 ,2 ,...$. Find all integers $m \ge 0$ such that $s_m = x_0 + x_1 + x_2 + ... + x_m$ is a power of $2$.