$\pi$ is irrational, and of course its digits are not a repeating sequence. However I cannot wrap my head around the following...

Is there a digit $x$ in $\pi$ such that the digits before are repeated in reverse order after that digit? $$\pi = 3.14159\ldots zyxxyz \ldots 951413 [\ldots]$$

In other words, is there a positive integer $n$ such that $\lfloor 10^n\pi\rfloor$ is palindromic?

$\pi$ has infinite digits, but it is unknown whether any sequence of digits will appear at some point. Moreover, this isn't just a requirement for $n$ digits appearing at some position, but for a sequence of $n$ digits has to appear at position $n$.