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A287556
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Start with 0 and repeatedly substitute 0->0132, 1->1320, 2->3201, 3->2013.
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9
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0, 1, 3, 2, 1, 3, 2, 0, 2, 0, 1, 3, 3, 2, 0, 1, 1, 3, 2, 0, 2, 0, 1, 3, 3, 2, 0, 1, 0, 1, 3, 2, 3, 2, 0, 1, 0, 1, 3, 2, 1, 3, 2, 0, 2, 0, 1, 3, 2, 0, 1, 3, 3, 2, 0, 1, 0, 1, 3, 2, 1, 3, 2, 0, 1, 3, 2, 0, 2, 0, 1, 3, 3, 2, 0, 1, 0, 1, 3, 2, 3, 2, 0, 1, 0, 1
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OFFSET
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1,3
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COMMENTS
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This is the fixed point of the morphism 0->0132, 1->1320, 2->3201, 3->2013 starting with 0. Let t be the (nonperiodic) sequence of positions of 0, and likewise, u for 1, v for 2, and w for 3; then t(n)/n -> 4, u(n)/n -> 4, v(n)/n -> 4, w(n)/n -> 4. Also, t(n) + u(n) + v(n) + w(n) = 16*n - 6 for n >= 1.
In the following guide to related sequences, column 1 indexes fixed points on {0,1,2,3}, and column 2 indicates position sequences of 0, 1, 2, 3. Those sequences therefore comprise a 4-way splitting of the positive integers.
Fixed points of morphisms: Position sequences:
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LINKS
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EXAMPLE
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First three iterations of the morphism:
0132
0132132020133201
0132132020133201132020133201013232010132132020132013320101321320
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MATHEMATICA
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s = Nest[Flatten[# /. {0 -> {0, 1, 3, 2}, 1 -> {1, 3, 2, 0}, 2 -> {3, 2, 0, 1}, 3 -> {2, 0, 1, 3}}] &, {0}, 9]; (* A287556 *)
Flatten[Position[s, 0]]; (* A287557 *)
Flatten[Position[s, 1]]; (* A287558 *)
Flatten[Position[s, 2]]; (* A287559 *)
Flatten[Position[s, 3]]; (* A287560 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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