# Indicator sequence/Prime numbers/Exercise

Let the sequence be given by

- Determine and .
- Does this sequence converge in ?

Let the sequence ${}{\left(x_{n}\right)}_{n\in \mathbb {N} }$ be given by

- ${}x_{n}={\begin{cases}1,\,{\text{ falls }}n{\text{ is a prime number }}\,,\\0\,{\text{ else}}\,.\end{cases}}\,$

- Determine ${}x_{117}$ and ${}x_{127}$.
- Does this sequence converge in ${}\mathbb {Q}$?