A305495 -id:A305495 - cp's OEIS frontend

A305490 Fixed point of the morphism 0->120, 1->110, 2->100.

1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 0, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 0, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 1, 0, 1, 0, 0, 1, 2, 0, 1, 1, 0, 1, 1

Offset: 1

Clark Kimberling, Jun 02 2018

This sequence is used to generate the anti-tribonacci sequence, A265389. The positions of 1 are also the positions of 0 in Stewart's choral sequence, A116178.

			1 -> 110 -> 110110120 -> ...

Clark Kimberling, Table of n, a(n) for n = 1..10000 [a(9842) corrected by Zhuorui He, Sep 04 2025]

Cf. A265389, A116178, A305495 (positions of 0), A189636 (positions of 1), A305496 (positions of 2).

Nest[Flatten[# /. {0 -> {1, 2, 0}, 1 -> {1, 1, 0}, 2 -> {1, 0, 0}}] &, {0}, 9];

A305490(n) = {n--;while(n%9==4,n=n\9);[1,1,0,1,1,0,1,2,0][n%9+1]}; \\ Zhuorui He, Sep 04 2025

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

Original entry on oeis.org

8, 17, 26, 35, 44, 53, 62, 68, 71, 80, 89, 98, 107, 116, 125, 134, 143, 149, 152, 161, 170, 179, 188, 197, 206, 215, 224, 230, 233, 242, 251, 260, 269, 278, 287, 296, 305, 311, 314, 323, 332, 341, 350, 359, 368, 377, 386, 392, 395, 404, 413, 422, 431, 440

Offset: 1

Clark Kimberling, Jun 02 2018

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.

			Fixed point: (1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, ... )
Positions of 0:  (3,6,9,12,15,18,21,23,  ... ) = A305495
Positions of 1:  (1,2,4,5,7,10,11,13,14, ... ) = A189636
Positions of 2:  (8,17,26,35,44,53,62,68,  ... ) = A305496

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A305490, A116178, A305495.

z = 120;
t = Nest[Flatten[# /. {0 -> {1, 2, 0}, 1 -> {1, 1, 0},
      2 -> {1, 0, 0}}] &, {0}, 9]; (* A305490 *)
Take[Flatten[Position[t, 0]], z] (* A305495  *)
Take[Flatten[Position[t, 1]], z] (* A116178 *)
Take[Flatten[Position[t, 2]], z] (* 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 *)

cp's OEIS Frontend

A305490 Fixed point of the morphism 0->120, 1->110, 2->100.

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