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A106826 Trajectory of 1 under the morphism 1->{2,1}, 2->{2,3}, 3->{4,3}, 4->{4,1}. 1

%I

%S 2,3,4,3,4,1,4,3,4,1,2,1,4,1,4,3,4,1,2,1,2,3,2,1,4,1,2,1,4,1,4,3,4,1,

%T 2,1,2,3,2,1,2,3,4,3,2,3,2,1,4,1,2,1,2,3,2,1,4,1,2,1,4,1,4,3,4,1,2,1,

%U 2,3,2,1,2,3,4,3,2,3,2,1,2,3,4,3,4,1,4,3,2,3,4,3,2,3,2,1,4,1,2,1,2,3,2,1,2

%N Trajectory of 1 under the morphism 1->{2,1}, 2->{2,3}, 3->{4,3}, 4->{4,1}.

%C This is the reverse of the morphism in A105500 and the trajectory of 1 actually starts with 2 instead of 1.

%H F. M. Dekking, <a href="http://dx.doi.org/10.1016/0001-8708(82)90066-4">Recurrent sets</a>, Advances in Mathematics, vol. 44, no. 1 (1982), 78-104.

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%t Nest[ Flatten[ # /. {1 -> {2, 1}, 2 -> {2, 3}, 3 -> {4, 3}, 4 -> {4, 1}}] &, {1}, 8] (*_Robert G. Wilson v_, Jun 20 2005 *)

%o (PARI) {a(n)=local(A);if(n<0, 0, n++; A=[2]; while(length(A)<n, A=concat(vector(length(A),k,[[2,1],[2,3],[4,3],[4,1]][A[k]]))); A[n])}

%Y Cf. A105500.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, May 20 2005

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Last modified July 18 10:35 EDT 2019. Contains 325138 sequences. (Running on oeis4.)