Let $(x_n)$ be a real sequence satisfying $ x_1=1 ,\space x_{n+1}=x_n+\dfrac{1}{x_n} ,\forall n \in \mathbb N$ , then can we find an expression for $[ x_n$] ( box-function) in terms of $n$ $,\forall n \in \mathbb N$ ? ( I have only been able to find that
$x_n^2>2n , \forall n>2$ and $lim \dfrac {x_n^2}{n}=2$)
