Does $\lfloor \tan (n)\rfloor =n$ have infinite roots? Background
This post can be understood as the gap between $\tan n$ and $n$ has no upper limit.
Does the sequence $n+\tan(n), n \in\mathbb{N}$ have a lower bound?
I want to know how close $\tan n$ can be to $n$.
I try to find some solution with difference less than 1.
$$|\tan n -n|<1$$
or similar
$$\lfloor \tan (n)\rfloor =n$$
$\lfloor x\rfloor$ means floor function.
I did a quick search for $n<10^7$ and found no solution other than $n = 0,1$
Question
Is there an infinite number of integers n that make the equation true, and how big will the next solution be?

According to https://oeis.org/A249836 (6th comment), $n = 0, 1$ are the only currently known solutions. You can also refer to https://oeis.org/A258024.
