Let $u_n$ be a sequence defined on natural numbers (the first term is $u_0$) and the terms are natural numbers ($u_n\in \mathbb{N}$ )
We defined the following sequences:
$\displaystyle \large x_n=u_{u_n}$ $\displaystyle \large y_n=u_{u_n}+1$
If we know that both $y_n$ and $x_n $ are arithmetic sequences ,how we can prove that $u_n $ is also arithmetic sequence