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A317953 Apply the morphism 1 -> {1, 2}, 2 -> {3,1}, 3 -> {1} n times to 1, and concatenate the resulting string.

%I A317953 #7 Aug 21 2018 10:21:35
%S A317953 1,12,1231,1231112,1231112121231,123111212123112311231112,
%T A317953 12311121212311231123111212311121231112121231,
%U A317953 123111212123112311231112123111212311121212311231112121231123111212123112311231112
%N A317953 Apply the morphism 1 -> {1, 2}, 2 -> {3,1}, 3 -> {1} n times to 1, and concatenate the resulting string.
%C A317953 For the tribonacci word A092782, each block b(n) (see A103269) is the concatenation of the three previous blocks: b(n) = b(n-1).b(n-2).b(n-3). Instead, here we have a(n) = a(n-1).a(n-3).a(n-2), as can be seen in the examples section below.
%D A317953 V. F. Sirvent, Semigroups and the self-similar structure of the flipped tribonacci substitution, Applied Math. Letters, 12 (1999), 25-29.
%e A317953 a(1): 1,
%e A317953 a(2): 12,
%e A317953 a(3): 1231,
%e A317953 a(4): 1231112,
%e A317953 a(5): 1231112121231,
%e A317953 a(6): 123111212123112311231112,
%e A317953 a(7): 12311121212311231123111212311121231112121231,
%e A317953 equals a(6).a(4).a(5), look:
%e A317953 a(6):123111212123112311231112,
%e A317953 a(4):                        1231112,
%e A317953 a(5):                               1231112121231,
%e A317953 a(8): 123111212123112311231112123111212311121212311231112121231123111212123112311231112
%e A317953 equals a(7).a(5).a(6), look:
%e A317953 a(7): 12311121212311231123111212311121231112121231,
%e A317953 a(5):                                             1231112121231,
%e A317953 a(6):                                                          123111212123112311231112,
%Y A317953 Cf. A100619 (the limiting string), A277735, A317953.
%Y A317953 A103269 is the analog for the word A092782.
%K A317953 nonn
%O A317953 1,2
%A A317953 _N. J. A. Sloane_, Aug 21 2018