This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A288577 #28 Jan 21 2018 09:36:22
%S A288577 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,
%T A288577 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,
%U A288577 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
%N 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,...}.
%C A288577 An analog of A104324 when "Fibonacci" is replaced with "tribonacci".
%C A288577 From _Kerry Mitchell_, Jul 01 2017: (Start)
%C A288577 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.):
%C A288577 0
%C A288577 0, 1, 2
%C A288577 0, 1, 2, 2, 3
%C A288577 0, 1, 2, 2, 3, 3, 3, 4, 5
%C A288577 0, 1, 2, 2, 3, 3, 3, 4, 5, 3, 4, 5, 3, 4, 5, 5, 6
%C A288577 etc.
%C A288577 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)
%D A288577 Kerry Mitchell, Posting to Sequence Fans Mailing List, Jun 30 2017
%H A288577 Kerry Mitchell, <a href="/A288577/b288577.txt">Table of n, a(n) for n = 0..13744</a>
%t A288577 SubstitutionSystem[{x_ -> If[Mod[x, 3] == 0, {x, x+1, x+2}, {x+1}]}, {0}, 7] // Last (* _Jean-François Alcover_, Jan 21 2018 *)
%Y A288577 Cf. A104324.
%K A288577 nonn
%O A288577 0,3
%A A288577 _N. J. A. Sloane_, Jul 01 2017
%E A288577 More terms from _Kerry Mitchell_, Jul 01 2017