# Talk:Automatic sequence

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## Definition

"the nth term can always be determined by applying a fixed and finite set of rules to the preceding n−1 terms" -- really? I think it's that the n'th term depends on the output of an FSA given the digits of n in some fixed base, and that this is not the same thing. Zarboublian (talk) 12:16, 29 May 2010 (UTC)

## Thue-Morse sequence

Allouche and Shallitt page 1752 say that this is 2-automatic. Why are arguing about calling it "automatic base 2"? Zarboublian (talk) 06:33, 12 June 2010 (UTC)

The actual phrase that I removed was "Thue-Morse sequence in base 2". This phrase implies that the Thue-Morse sequence could be expressed in some other base - so you could, for example, have a "Thue-Morse sequence in base 5", and it would be a different sequence from the "Thue-Morse sequence in base 2" (just as the number five is 101 in base 2 but 10 in base 5). This is not true; there is only one Thue-Morse sequence, it is a 2-automatic sequence, but the sequence itself is not expressed in a particular base. Gandalf61 (talk)