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In mathematics, the Prouhet–Thue–Morse constant, named for Eugène Prouhet, Axel Thue, and Marston Morse, is the number—denoted by τ—whose binary expansion 0.01101001100101101001011001101001... is given by the Thue–Morse sequence. That is,
where tn is the n element of the Prouhet–Thue–Morse sequence.
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