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A245555 Trajectory of 1 under morphism 1 -> 1,2; 2 -> 2,3; 3 -> 3,1. 2

%I

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

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

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

%N Trajectory of 1 under morphism 1 -> 1,2; 2 -> 2,3; 3 -> 3,1.

%C The morphism 1->1,2; 2->2,1 gives the {1,2} version of the Thue-Morse sequence A001285, cf. A010060.

%C The morphism 0->0,1; 1->1,2; 2->2,0 gives the generalized Thue-Morse sequence A071858.

%H Chai Wah Wu, <a href="/A245555/b245555.txt">Table of n, a(n) for n = 1..10000</a>

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

%t Nest[ Function[ l, {Flatten[(l /. {1 -> {1, 2}, 2 -> {2, 3}, 3 -> {3, 1}})] }], {1}, 9]

%o (PARI) {a(n) = my(v = [1]); if( n<1, 0, while( #v<n, v = concat( vector(#v, i, [[1,2], [2,3], [3,1]] [v[i]]))); v[n])}; /* _Michael Somos_, Aug 05 2014 */

%Y Cf. A001285, A010060, A071858, A092782, A105083, A245553, A245554.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Aug 03 2014

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Last modified December 10 04:15 EST 2019. Contains 329885 sequences. (Running on oeis4.)