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A288577
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Image of 0 under repeated application of the morphism phi = {x -> x,x+1,x+2 if x mod 3 = 0; x -> x+1 if x mod 3 = 1 or 2, for x = 0,1,2,3,...}.
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3
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0, 1, 2, 2, 3, 3, 3, 4, 5, 3, 4, 5, 3, 4, 5, 5, 6, 3, 4, 5, 5, 6, 3, 4, 5, 5, 6, 6, 6, 7, 8, 3, 4, 5, 5, 6, 6, 6, 7, 8, 3, 4, 5, 5, 6, 6, 6, 7, 8, 6, 7, 8, 6, 7, 8, 8, 9, 3, 4, 5, 5, 6, 6, 6, 7, 8, 6, 7, 8, 6, 7, 8, 8, 9, 3, 4, 5, 5, 6, 6, 6, 7, 8, 6, 7, 8, 6, 7, 8, 8, 9, 6, 7, 8, 8, 9, 6, 7, 8, 8, 9, 9, 9, 10, 11
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OFFSET
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0,3
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COMMENTS
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An analog of A104324 when "Fibonacci" is replaced with "tribonacci".
This is the limit of a series of iterations. The length of each iteration is given by A000213, beginning with the second term of that sequence (1, 3, 5, 9, 17, etc.):
0
0, 1, 2
0, 1, 2, 2, 3
0, 1, 2, 2, 3, 3, 3, 4, 5
0, 1, 2, 2, 3, 3, 3, 4, 5, 3, 4, 5, 3, 4, 5, 5, 6
etc.
When written in blocks this way, each subsequent block is the concatenation of the previous block, the third-previous block with each term incremented by 3, and the second-previous block, with each term incremented by 3. (End)
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REFERENCES
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Kerry Mitchell, Posting to Sequence Fans Mailing List, Jun 30 2017
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LINKS
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MATHEMATICA
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SubstitutionSystem[{x_ -> If[Mod[x, 3] == 0, {x, x+1, x+2}, {x+1}]}, {0}, 7] // Last (* Jean-François Alcover, Jan 21 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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