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%I #20 Oct 19 2020 23:14:49
%S 0,0,0,0,0,1,0,0,0,1,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,
%T 0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,
%U 0,1,1,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,1,0,0,1,0,0
%N Image of A053838 under the morphism 0 -> 0000, 1 -> 0100, 2 -> 0110.
%H Michel Rigo, <a href="https://doi.org/10.1016/j.indag.2016.11.018">Relations on words</a>, Indagationes Mathematicae, Vol. 28, No. 1 (2017), pp. 183-204, <a href="https://arxiv.org/abs/1602.03364">arXiv preprint</a>, arXiv:1602.03364 [cs.FL], 2016.
%t terms = 100; Clear[f];
%t f[k_] := f[k] = (A053838 = SubstitutionSystem[{0 -> {0, 1, 2}, 1 -> {1, 2, 0}, 2 -> {2, 0, 1}}, {0}, k] // Last; SubstitutionSystem[{0 -> {0, 0, 0, 0}, 1 -> {0, 1, 0, 0}, 2 -> {0, 1, 1, 0}}, A053838, 1] // Last // PadRight[#, terms]& // Take[#, terms]&);
%t f[k = 1]; f[k++];
%t While[Print["k = ", k]; f[k] != f[k - 1], k++];
%t f[k] (* _Jean-François Alcover_, Nov 16 2018 *)
%Y Cf. A053838.
%K nonn
%O 0
%A _N. J. A. Sloane_, Dec 30 2016
%E More terms from _Jean-François Alcover_, Nov 16 2018
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