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 A287523 Fixed point starting with 1 of the morphism 0->01, 1->101. 3
 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS Previous name was: 0-limiting word of reversed iterates of the mapping 0->1, 1->10, starting with 1. The first eight iterates of the mapping 0->1, 1->10, starting with 1, are these words: 1 10 101 10110 10110101 1011010110110 101101011011010110101 1011010110110101101011011010110110 with limit the infinite Fibonacci word A005614. The corresponding reversed iterates are as follows: 1 01 101 01101 10101101 0110110101101 101011010110110101101 0110110101101101011010110110101101 The 0-limiting word is the limit of the n-th iterates for n == 0 mod 2. (The 1-limiting word is A189479) Let sigma be the morphism 0->1, 1->10. Then sigma^2 is given by 0->10, 1->101. The time reversal tau of sigma^2 is given by 0->01, 1->101, and tau^n(1) is equal to the n == 0 mod 2 reversed iterates above. Thus we obtain A189479. - Michel Dekking, Aug 09 2017 The fixed point starting with 0 is A189479. - Michel Dekking, Sep 30 2019 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: 1 101 10101101 101011010110110101101 MATHEMATICA z = 12; (*number of iterates*) s = {0}; w[0] = StringJoin[Map[ToString, s]]; w[n_] := StringReplace[w[n - 1], {"0" -> "1", "1" -> "10"}]; r[n_] := StringReverse[w[n]]; TableForm[Table[r[n], {n, 0, 8}]] rw = ToCharacterCode[r[z]] - 48; (* A287523 if z even A288243 if z odd *) p0 = Flatten[Position[rw, 0]]; (* A026356 if z even, A007066 if z odd *) p1 = Flatten[Position[rw, 1]]; (* A189662 if z even, A099267 if z odd *) CROSSREFS Cf. A005614, A026356, A189479, A189662. Sequence in context: A283963 A131670 A188044 * A288932 A155482 A174205 Adjacent sequences: A287520 A287521 A287522 * A287524 A287525 A287526 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jul 10 2017 EXTENSIONS Name changed by Michel Dekking, Sep 30 2019 STATUS approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)