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A305495 Positions of 0 in the fixed point of the morphism 0->120, 1->110, 2->100 applied to 1 (as in A305490).

%I A305495 #9 Jul 16 2024 02:34:35
%S A305495 3,6,9,12,15,18,21,23,24,27,30,33,36,39,42,45,48,50,51,54,57,60,63,66,
%T A305495 69,72,75,77,78,81,84,87,90,93,96,99,102,104,105,108,111,114,117,120,
%U A305495 123,126,129,131,132,135,138,141,144,147,150,153,156,158,159
%N A305495 Positions of 0 in the fixed point of the morphism 0->120, 1->110, 2->100 applied to 1 (as in A305490).
%C A305495 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 A305495 Clark Kimberling, <a href="/A305495/b305495.txt">Table of n, a(n) for n = 1..10000</a>
%e A305495 Fixed point: (1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, ... )
%e A305495 Positions of 0:  (3,6,9,12,15,18,21,23,  ... ) = A305495
%e A305495 Positions of 1:  (1,2,4,5,7,10,11,13,14, ... ) = A189636
%e A305495 Positions of 2:  (8,17,26,35,44,53,62,68,  ... ) = A305496
%t A305495 z = 120;
%t A305495 t = Nest[Flatten[# /. {0 -> {1, 2, 0}, 1 -> {1, 1, 0},
%t A305495       2 -> {1, 0, 0}}] &, {0}, 9]; (* A305490 *)
%t A305495 Take[Flatten[Position[t, 0]], z] (* A305495  *)
%t A305495 Take[Flatten[Position[t, 1]], z] (* A116178 *)
%t A305495 Take[Flatten[Position[t, 2]], z] (* A305496 *)
%Y A305495 Cf. A305490, A116178, A305496.
%K A305495 nonn,easy
%O A305495 1,1
%A A305495 _Clark Kimberling_, Jun 02 2018