High Quality Content by WIKIPEDIA articles! In mathematics, the Thue–Morse sequence, or Prouhet–Thue–Morse sequence, is a binary sequence that begins: 0?1?10?1001?10010110?1001011001101001.... Any other ordered pair of symbols may be used instead of 0 and 1; the logical structure of the Thue–Morse sequence does not depend on the symbols that are used to represent it. To compute the nth element tn, write the number n in binary. If the number of ones in this binary expansion is odd then tn = 1, if even then tn = 0. For this reason John H. Conway et al. call numbers n satisfying tn = 1 odious numbers and numbers for which tn = 0 evil numbers.

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