The exercise is from Stein-Shakarchi's Real Analysis (Chapter 1, ex. 24). It asks about an enumeration of the rationals $\left\{r_{n}\right\}_{n\geq 1}$ such that the complement of $\bigcup_{n=1}^{\infty}{\left(r_{n}-\frac{1}{n},r_{n}+\frac{1}{n}\right)}$ in $\mathbb{R}$ is non-empty.
While, I understand that we probably need some enumeration of the rationals such that the only rationals outside a fixed bounded interval are of the form $r_{m^{2}}$ for some $m$, I'm having trouble seeing how to get such an enumeration.
As always, help is very appreciated :)