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A285080
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0-limiting word of the morphism 0->10, 1-> 011.
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6
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0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1
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OFFSET
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1
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COMMENTS
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The morphism 0->10, 1->011 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 10 -> 01110 -> 1001101101110 -> 0111010011011100110111001101101110; if the number of iterations is odd, the 1-word evolves from 0 -> 10 -> 01110 -> 1001101101110, as in A285083.
Let v(n) = position of n-th 1. Then v(n)/n -> (1+sqrt(5))/2, the golden ratio (A001622); see A285082.
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 1..10000
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MATHEMATICA
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s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {0, 1, 1}}] &, {0}, 14]; (* A285080 *)
Flatten[Position[s, 0]]; (* A285081 *)
Flatten[Position[s, 1]]; (* A285082 *)
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CROSSREFS
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Cf. A001622, A285081, A285082, A285083.
Sequence in context: A265333 A159637 A095076 * A167392 A190201 A189702
Adjacent sequences: A285077 A285078 A285079 * A285081 A285082 A285083
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, Apr 19 2017
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STATUS
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approved
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