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

Author

Clark Kimberling, Jun 02 2018

Keywords

• nonn
• easy
• changed

Comments

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.

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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