  The Frobenius number $g(S)$ of a set $S$ of non-negative integers with $\gcd
1$ is the largest integer not expressible as a linear combination of elements
of $S$. Given a sequence ${\bf s} = (s_i)_{i \geq 0}$, we can define the
associated sequence $G_{\bf s} (i) = g(\{ s_i,s_{i+1},\ldots \})$. In this
paper we compute $G_{\bf s} (i)$ for some classical automatic sequences: the
evil numbers, the odious numbers, and the lower and upper Wythoff sequences. In
contrast with the usual methods, our proofs are based largely on automata
theory and logic.
