A191269 Fixed point of the morphism 0 -> 001, 1 -> 02, 2 -> 01.

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

Offset: 1

Author

Clark Kimberling, May 28 2011

Keywords

• nonn

Comments

See A191250.

Proof of Kimberling's conjecture on the positions of 0 in this sequence: consider the letter to letter projection pi given by pi(0) = 0, pi(1) = 1, pi(2) = 1. Then pi sigma = tau pi, where tau is the morphism on {0,1} given by tau(0) = 001, tau(1) = 01. It follows that pi(a) = x, where x = A188432 is the fixed point of tau. Note that the positions of zero in a = A191269 are equal to the positions of zero in x. Since x is the infinite Fibonacci word with a zero in front, it follows that these positions are given by A026351. - Michel Dekking, Aug 24 2019

Crossrefs

Cf. A191250, A191270, A191271.

Programs

Mathematica

t = Nest[Flatten[# /. {0 -> {0, 0, 1}, 1 -> {0, 2}, 2 -> {0, 1}}] &, {0}, 7] (* A191269 *)
Flatten[Position[t, 0]]  (* A026351, 1+lower Wythoff sequence, conjectured *)
Flatten[Position[t, 1]] (* A191270 *)
Flatten[Position[t, 2]] (* A191271 *)