  The $p$-adic Littlewood conjecture (PLC) states that $\liminf_{q\to\infty}
q\cdot |q|_p \cdot ||qx|| = 0$ for every prime $p$ and every real $x$. Let
$w_{CF}(x)$ be an infinite word composed of the continued fraction expansion of
$x$ and let $\mathrm{T}$ be the standard left shift map. Assuming that $x$ is a
counterexample to PLC we get several restrictions on limit elements of the
sequence $\{\mathrm{T}^n w_{CF}(x)\}_{n\in\mathbb{N}}$. As a consequence we
show that for any such limit element $w$ we must have $\lim_{n\to\infty} P(w,n)
- n = \infty$ where $P(w,n)$ is a word complexity of $w$. We also show that $w$
can not be among a certain collection of recursively constructed words.
