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 A289034 Fixed point of the morphism 0->010, 1->10 starting with 1. 3
 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 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, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS Old name was: 1-limiting word of reversed iterates of the mapping 0->01, 1->0, starting with 0. The first seven iterates of the mapping 0->01, 1->0, starting with 0, are: 0 01 010 01001 01001010 0100101001001 010010100100101001010 with limit the infinite Fibonacci word A003849. The corresponding reversed iterates are as follows: 0 10 010 10010 01010010 1001001010010 010100101001001010010 The 1-limiting word is the limit of the n-th iterates for n == 1 mod 2. (The 0-limiting word is A189661.) There is a simple way to construct this. Let sigma be the time-reversed Fibonacci morphism, i.e., the morphism sigma: 0->10, 1->0. Then sigma^2 is given by 0->010, 1->10, and sigma^2 has two fixed points. The fixed point starting with 1 is the present sequence. - Michel Dekking, Oct 18 2018 LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 EXAMPLE The first four n-th reversed iterates for n == 1 mod 2 are these: 10 10010 1001001010010 1001001010010010100101001001010010 MATHEMATICA z = 13; (*number of iterates*) s = {0}; w[0] = StringJoin[Map[ToString, s]]; w[n_] := StringReplace[w[n - 1], {"0" -> "01", "1" -> "0"}]; r[n_] := StringReverse[w[n]]; TableForm[Table[r[n], {n, 0, 8}]] rw = ToCharacterCode[r[z]] - 48 (* A289034 *) p0 = Flatten[Position[rw, 0]]; (* A099267 *) p1 = Flatten[Position[rw, 1]]; (* A007066 *) CROSSREFS Cf. A003849, A189661, A099267, A007066, A287523 (binary complement), A188432. Sequence in context: A068429 A285208 A260444 * A011747 A089013 A188374 Adjacent sequences: A289031 A289032 A289033 * A289035 A289036 A289037 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jul 10 2017 EXTENSIONS Name changed by Michel Dekking, Oct 20 2018 STATUS approved

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Last modified August 9 08:03 EDT 2024. Contains 375034 sequences. (Running on oeis4.)