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A214640 A ternary sequence : closed under 1 -> 123, 2 -> 12, 3 -> 2 . Start with 1 .

%I A214640 #18 Nov 04 2020 05:55:59
%S A214640 1,2,3,1,2,2,1,2,3,1,2,1,2,1,2,3,1,2,2,1,2,3,1,2,1,2,3,1,2,1,2,3,1,2,
%T A214640 2,1,2,3,1,2,1,2,1,2,3,1,2,2,1,2,3,1,2,1,2,3,1,2,2,1,2,3,1,2,1,2,3,1,
%U A214640 2,2,1,2,3,1,2,1,2,1,2,3,1,2,2,1,2,3,1,2,1,2,3,1,2,1,2,3,1,2,2,1,2,3,1,2,1,2,1,2,3,1,2,2,1,2,3,1,2
%N A214640 A ternary sequence : closed under 1 -> 123, 2 -> 12, 3 -> 2 . Start with 1 .
%H A214640 Alois P. Heinz, <a href="/A214640/b214640.txt">Table of n, a(n) for n = 1..10000</a>
%e A214640 Start: 1
%e A214640 Rules:
%e A214640   1 --> 123
%e A214640   2 --> 12
%e A214640   3 --> 2
%e A214640 -------------
%e A214640 0:   (#=1)
%e A214640   1
%e A214640 1:   (#=3)
%e A214640   123
%e A214640 2:   (#=6)
%e A214640   123122
%e A214640 3:   (#=13)
%e A214640   1231221231212
%e A214640 4:   (#=29)
%e A214640   12312212312121231221231212312
%e A214640 5:   (#=64)
%e A214640   1231221231212123122123121231212312212312121231221231212312212312
%p A214640 S:= proc(n) option remember; `if`(n=0, [1], subs(x=[1, 2, 3][],
%p A214640        y=[1, 2][], z=2, subs(1=x, 2=y, 3=z, S(n-1))))
%p A214640     end:
%p A214640 a:= proc(n) local k;
%p A214640        for k while nops(S(k))<n do od; S(k)[n]
%p A214640     end:
%p A214640 seq(a(n), n=1..100);  # _Alois P. Heinz_, Jul 28 2012
%t A214640 SubstitutionSystem[{1 -> {1, 2, 3}, 2 -> {1, 2}, 3 -> {2}}, {1}, 6] // Last (* _Jean-François Alcover_, Nov 04 2020 *)
%Y A214640 Cf. A214260, A214641, A214642, A214644.
%K A214640 nonn,easy
%O A214640 1,2
%A A214640 _Philippe Deléham_, Jul 23 2012