Hyperquadratic continued fractions and automatic sequences

We show that three different families of hyperquadratic elements, studied in the literature, have the following property: For these elements, the leading coefficients of the partial quotients in their continued fraction expansion form 2-automatic sequences. We also show that this is not true for algebraic elements in F(q)F(q) in general. Indeed, we use an element studied by Mills and Robbins as counterexample. This element is algebraic in F(3)F(3) but the principal coefficients of the partial quotients do not form an automatic sequence.