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A133162
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Trajectory of 1 under the morphism 1 -> {1,1,2,1}, 2 -> {2}.
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4
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1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1
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OFFSET
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1,3
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COMMENTS
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It can be shown that this is lim_{t -> oo} S_t, where S_0 = 1, S_{t+1} = S_t S_t 2 S_t.
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LINKS
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FORMULA
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Denote the sequence by a(1), a(2), ...
Block t, that is, S_t, extends from n=1 through n=(3^(t+1)-1)/2.
Given n, to find a(n): first find t from
p = (3^t-1)/2 < n <= (3^(t+1)-1)/2.
Then if n=3^t, a(n) = 2. Otherwise, a(n) = a(n'), where
n' = n-p if n<3^t, otherwise n' = n-2p-1.
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MATHEMATICA
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Nest[Function[l, {Flatten[(l /. {1 -> {1, 1, 2, 1}, 2 -> {2} })] }], {1}, 5] (* Georg Fischer, Jul 19 2019 *)
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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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