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A287571
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Start with 0 and repeatedly substitute 0->0312, 1->3120, 2->1203, 3->2031.
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6
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0, 3, 1, 2, 2, 0, 3, 1, 3, 1, 2, 0, 1, 2, 0, 3, 1, 2, 0, 3, 0, 3, 1, 2, 2, 0, 3, 1, 3, 1, 2, 0, 2, 0, 3, 1, 3, 1, 2, 0, 1, 2, 0, 3, 0, 3, 1, 2, 3, 1, 2, 0, 1, 2, 0, 3, 0, 3, 1, 2, 2, 0, 3, 1, 3, 1, 2, 0, 1, 2, 0, 3, 0, 3, 1, 2, 2, 0, 3, 1, 0, 3, 1, 2, 2, 0
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OFFSET
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1,2
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COMMENTS
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This is the fixed point of the morphism 0->0231, 1->2310, 2->3102, 3->1023 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. See A287556 for a guide to related sequences.
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 1..20000
Index entries for sequences that are fixed points of mappings
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FORMULA
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a(n) = 4n - A287574(n) for n >= 1.
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EXAMPLE
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First three iterations of the morphism:
0312
0312203131201203
0312203131201203120303122031312020313120120303123120120303122031
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MATHEMATICA
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s = Nest[Flatten[# /. {0 -> {0, 3, 1, 2}, 1 -> {3, 1, 2, 0}, 2 -> {1, 2, 0, 3}, 3 -> {2, 0, 3, 1}}] &, {0}, 9]; (* A287571 *)
Flatten[Position[s, 0]]; (* A287572 *)
Flatten[Position[s, 1]]; (* A287573 *)
Flatten[Position[s, 2]]; (* A287574 *)
Flatten[Position[s, 3]]; (* A287575 *)
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CROSSREFS
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Cf. A287572, A287573, A287574, A287575.
Sequence in context: A070773 A046804 A263211 * A214316 A236452 A056529
Adjacent sequences: A287568 A287569 A287570 * A287572 A287573 A287574
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, May 31 2017
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STATUS
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approved
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