In an earlier talk the complexity of an automatic sequence was presented as the minimal size of an automaton describing the sequence. More precisely, the n-th element of the binary sequence is 1 if and only if the binary representation of n is accepted by the automaton. On this notion some main properties were investigated. In the meantime a paper on this work has been accepted for the LATA 2020 conference, and was honored by the best paper award. After a recap of the main notions and properties, in this talk the focus will be on how to compute the corresponding minimal automaton automatically from a prefix of the sequence, by means of SMT solving, and on criteria on how long this prefix should be.