We define a sequence with $a_{1}=850$ and

$$
a_{n+1}=\frac{a_{n}^{2}}{a_{n}-1}
$$

for $n \geq 1$. Determine all values of $n$ for which $\left\lfloor a_{n}\right\rfloor=2024$.
Here, the floor $\lfloor a\rfloor$ of a real number $a$ denotes the greatest integer less than or equal to $a$.