A287451 - OEIS

%I #9 Nov 27 2024 13:03:42

%S 0,1,2,2,0,1,1,2,0,1,2,0,0,1,2,2,0,1,2,0,1,1,2,0,0,1,2,2,0,1,1,2,0,0,

%T 1,2,0,1,2,2,0,1,1,2,0,1,2,0,0,1,2,2,0,1,1,2,0,0,1,2,2,0,1,2,0,1,1,2,

%U 0,0,1,2,0,1,2,2,0,1,1,2,0,1,2,0,0,1

%N Start with 0 and repeatedly substitute 0->012, 1->201, 2->120.

%C This is the fixed point of the morphism 0->012, 1->201, 2->120 starting with 0.  Let u be the (nonperiodic) sequence of positions of 0, and likewise, v for 1 and w for 2; then u(n)/n -> 3, v(n)/n -> 3,  w(n)/n -> 3.

%C See A287385 for a guide to related sequences.

%H Clark Kimberling, <a href="/A287451/b287451.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>

%e First three iterations of the morphism:  012, 012201120, 012201120120012201201120012.

%t s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 0, 1}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287451*)

%t Flatten[Position[s, 0]]; (*A287452*)

%t Flatten[Position[s, 1]]; (*A287453*)

%t Flatten[Position[s, 2]]; (*A287454*)

%t SubstitutionSystem[{0->{0,1,2},1->{2,0,1},2->{1,2,0}},{0},{5}][[1]] (* _Harvey P. Dale_, Nov 27 2024 *)

%Y Cf. A287385, A287452, A287453, A287454.

%K nonn,easy,changed

%O 1,3

%A _Clark Kimberling_, May 30 2017