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 A285966 {11->1}-transform of the Thue-Morse word A010060. 3
 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS From Michel Dekking, Mar 15 2019: (Start) This sequence is a morphic sequence, i.e., a letter-to-letter image of a fixed point of a morphism. Coding: 0 followed by 0 by 0, 0 followed by 1 by 2, 1 by 1 if 1 was in 010 in the TM word, 1 by 3 if it was the image of 11 in the TM word. It then follows that (a(n)) is the letter to letter image 0->0, 1->1, 2->0, 3->1 of the unique fixed point of the morphism 0 -> 21 1 -> 0 2 -> 23 3 -> 210. Explanation of (the more difficult) first and last productions: 010 -> 011001 by the TM morphism, which is coded to 2302. Here the 3 is put in the production 2 -> 23, the 0 is from the production 1 -> 0, and the final 2 is taken care of in either the production 0 -> 21, or the production 2 -> 23. For the last production, note that 0110 -> 01101001 by the TM morphism, which is coded to 232102. Here the prefix 23 is taken care of by the production 2 -> 23, then 11 coded by 3 gives 210, and the final 2 comes from the final 0 in 0110. (End) LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 EXAMPLE As a word, A010060 = 0110100110010110100101100..., and replacing each 11 by 1 gives 01010010010101001010010100100101... MATHEMATICA s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* Thue-Morse, A010060 *) w = StringJoin[Map[ToString, s]] w1 = StringReplace[w, {"11" -> "1"}] st = ToCharacterCode[w1] - 48 (* A285966 *) Flatten[Position[st, 0]] (* A285967 *) Flatten[Position[st, 1]] (* A285968 *) CROSSREFS Cf. A010060, A285967, A285968. Sequence in context: A073424 A135993 A334414 * A215530 A241422 A189661 Adjacent sequences: A285963 A285964 A285965 * A285967 A285968 A285969 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 06 2017 STATUS approved

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Last modified March 5 10:09 EST 2024. Contains 370548 sequences. (Running on oeis4.)