This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A191269 #10 Aug 25 2019 10:18:33
%S A191269 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,
%T A191269 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,
%U A191269 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
%N A191269 Fixed point of the morphism 0 -> 001, 1 -> 02, 2 -> 01.
%C A191269 See A191250.
%C A191269 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
%t A191269 t = Nest[Flatten[# /. {0 -> {0, 0, 1}, 1 -> {0, 2}, 2 -> {0, 1}}] &, {0}, 7] (* A191269 *)
%t A191269 Flatten[Position[t, 0]] (* A026351, 1+lower Wythoff sequence, conjectured *)
%t A191269 Flatten[Position[t, 1]] (* A191270 *)
%t A191269 Flatten[Position[t, 2]] (* A191271 *)
%Y A191269 Cf. A191250, A191270, A191271.
%K A191269 nonn
%O A191269 1,8
%A A191269 _Clark Kimberling_, May 28 2011