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A191254
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Fixed point of the morphism 0 -> 01, 1 -> 02, 2 -> 01.
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3
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0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2
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OFFSET
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1,4
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COMMENTS
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For related sequences, see notes in the Mathematica program.
The asymptotic density of the occurrences of k = 0, 1 and 2 is 1/2, 1/3 and 1/6, respectively. The asymptotic mean of this sequence is 2/3. - Amiram Eldar, May 31 2024
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LINKS
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FORMULA
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Recurrence: a(2n-1) = 0, a(2n) = 1, 2, 1 for a(n) = 0, 1, 2 respectively.
a(n) = 0 for odd n; a(n) = 1 for even n such that v2(n) is odd; a(n) = 2 for even n such that v2(n) is even, where v2(n) = A007814(n) is the 2-adic valuation of n. (End)
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MATHEMATICA
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t = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0, 2}, 2 -> {0, 1}}] &, {0}, 9] (* A191254 *)
Flatten[Position[t, 0]] (* A005408, the odds *)
a = Flatten[Position[t, 1]] (* A036554 *)
b = Flatten[Position[t, 2]] (* A108269 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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