Lesson plan
Automatic sequence
In mathematics and theoretical computer science, an automatic sequence (also called a k-automatic sequence or a k-recognizable sequence when one wants to indicate that the base of the numerals used is k) is an infinite sequence of terms characterized by a finite automaton. The n-th term of an automatic sequence a(n) is a mapping of the final state reached in a finite automaton accepting the digits of the number n in some fixed base k. An automatic set is a set of non-negative integers S for which the sequence of values of its characteristic function χ S is an automatic sequence; that is, S is k-automatic if χ S (n) is k-automatic, where χ S (n) = 1 if n \in S and 0 otherwise.
Article summary
In mathematics and theoretical computer science, an automatic sequence (also called a k-automatic sequence or a k-recognizable sequence when one wants to indicate that the base of the numerals used is k) is an infinite sequence of terms characterized by a finite automaton. The n-th term of an automatic sequence a(n) is a mapping of the final state reached in a finite automaton accepting the digits of the number n in some fixed base k. An automatic set is a set of non-negative integers S for which the sequence of values of its characteristic function χ S is an automatic sequence; that is, S is k-automatic if χ S (n) is k-automatic, where χ S (n) = 1 if n \in S and 0 otherwise.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.