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A305496 Positions of 2 in the fixed point of the morphism 0->120, 1->110, 2->100 applied to 1 (as in A305490).

%I A305496 #10 Jul 16 2024 02:34:57
%S A305496 8,17,26,35,44,53,62,68,71,80,89,98,107,116,125,134,143,149,152,161,
%T A305496 170,179,188,197,206,215,224,230,233,242,251,260,269,278,287,296,305,
%U A305496 311,314,323,332,341,350,359,368,377,386,392,395,404,413,422,431,440
%N A305496 Positions of 2 in the fixed point of the morphism 0->120, 1->110, 2->100 applied to 1 (as in A305490).
%C A305496 Let u, v, w be the position sequences of 0,1,2 in A305490.  They partition the positive integers, and v is also the position sequence of 0 in Stewart's choral sequence, A116178.
%H A305496 Clark Kimberling, <a href="/A305496/b305496.txt">Table of n, a(n) for n = 1..10000</a>
%e A305496 Fixed point: (1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, ... )
%e A305496 Positions of 0:  (3,6,9,12,15,18,21,23,  ... ) = A305495
%e A305496 Positions of 1:  (1,2,4,5,7,10,11,13,14, ... ) = A189636
%e A305496 Positions of 2:  (8,17,26,35,44,53,62,68,  ... ) = A305496
%t A305496 z = 120;
%t A305496 t = Nest[Flatten[# /. {0 -> {1, 2, 0}, 1 -> {1, 1, 0},
%t A305496       2 -> {1, 0, 0}}] &, {0}, 9]; (* A305490 *)
%t A305496 Take[Flatten[Position[t, 0]], z] (* A305495  *)
%t A305496 Take[Flatten[Position[t, 1]], z] (* A116178 *)
%t A305496 Take[Flatten[Position[t, 2]], z] (* A305496 *)
%t A305496 Position[SubstitutionSystem[{0->{1,2,0},1->{1,1,0},2->{1,0,0}},{1},{6}][[1]],2]//Flatten (* _Harvey P. Dale_, May 03 2022 *)
%Y A305496 Cf. A305490, A116178, A305495.
%K A305496 nonn,easy
%O A305496 1,1
%A A305496 _Clark Kimberling_, Jun 02 2018