  We give a dynamical construction of an infinite sequence of distinct totally
$p$-adic algebraic numbers whose Weil heights tend to the limit $\frac{\log
p}{p-1}$, thus giving a new proof of a result of Bombieri-Zannier. The proof is
essentially equivalent to the explicit calculation of the Arakelov-Zhang
pairing of the maps $\sigma(x)=x^2$ and $\phi_p(x)=\frac{1}{p}(x^p-x)$.
