A305496 - OEIS

%I #10 Jul 16 2024 02:34:57

%S 8,17,26,35,44,53,62,68,71,80,89,98,107,116,125,134,143,149,152,161,

%T 170,179,188,197,206,215,224,230,233,242,251,260,269,278,287,296,305,

%U 311,314,323,332,341,350,359,368,377,386,392,395,404,413,422,431,440

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

%C 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 Clark Kimberling, <a href="/A305496/b305496.txt">Table of n, a(n) for n = 1..10000</a>

%e Fixed point: (1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, ... )

%e Positions of 0:  (3,6,9,12,15,18,21,23,  ... ) = A305495

%e Positions of 1:  (1,2,4,5,7,10,11,13,14, ... ) = A189636

%e Positions of 2:  (8,17,26,35,44,53,62,68,  ... ) = A305496

%t z = 120;

%t t = Nest[Flatten[# /. {0 -> {1, 2, 0}, 1 -> {1, 1, 0},

%t       2 -> {1, 0, 0}}] &, {0}, 9]; (* A305490 *)

%t Take[Flatten[Position[t, 0]], z] (* A305495  *)

%t Take[Flatten[Position[t, 1]], z] (* A116178 *)

%t Take[Flatten[Position[t, 2]], z] (* A305496 *)

%t 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 Cf. A305490, A116178, A305495.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 02 2018