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 A288577 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,...}. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS An analog of A104324 when "Fibonacci" is replaced with "tribonacci". From Kerry Mitchell, Jul 01 2017: (Start) 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) REFERENCES Kerry Mitchell, Posting to Sequence Fans Mailing List, Jun 30 2017 LINKS Kerry Mitchell, Table of n, a(n) for n = 0..13744 MATHEMATICA SubstitutionSystem[{x_ -> If[Mod[x, 3] == 0, {x, x+1, x+2}, {x+1}]}, {0}, 7] // Last (* Jean-François Alcover, Jan 21 2018 *) CROSSREFS Cf. A104324. Sequence in context: A029095 A212295 A194315 * A159270 A165103 A281579 Adjacent sequences:  A288574 A288575 A288576 * A288578 A288579 A288580 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 01 2017 EXTENSIONS More terms from Kerry Mitchell, Jul 01 2017 STATUS approved

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Last modified April 7 10:26 EDT 2020. Contains 333300 sequences. (Running on oeis4.)