I am a beginner to computability theory and curently reading Pour-El and Richard Computability in Analysis and Physics, Chapter $0$.
At page $14,$ they provided a definition for computable sequence of rational numbers:
A sequence $\{r_n\}$ of rational numbers is computable if there exist three recursive functions $a,b,s$ from $\mathbb{N}$ to $\mathbb{N}$ such that $b(k)\neq 0$ for all $k$ and $$r_k = (-1)^{s(k)}\frac{a(k)}{b(k)} \quad \text{for all }k.$$
I have trouble understanding the definition above. In particular,
Question: What are some examples of computable sequence of rational numbers?