A285518 - OEIS

%I #17 Feb 28 2021 00:44:47

%S 1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,

%T 0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,

%U 0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1

%N {00->0, 11->1}-transform of A285504.

%C As a word, A285504 = 1111001100111111001100111111001100111111..., so that the substitutions 00-> and 11->1 leave 110101110101110101110101010101011101...

%C The sequence can also be given as the 1-limiting word of the morphism 0->11, 1->0101. The reason is that the generating morphism for A285504 is the morphism 0->11, 1-> 0011, which generates a 2-block morphism 00->11 11, 11->00 11 00 11. - _Michel Dekking_, Feb 28 2021

%C See A285519 and A285520 for conjectured connections to the golden ratio.

%H Clark Kimberling, <a href="/A285518/b285518.txt">Table of n, a(n) for n = 1..10000</a>

%t s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 0, 1, 1}}] &, {0}, 7] (* A285504 *)

%t w = StringJoin[Map[ToString, s]]

%t w1 = StringReplace[w, {"11" -> "1", "00" -> "0"}]

%t s1 = ToCharacterCode[w1] - 48 (* A285518 *)

%t Flatten[Position[s1, 0]]  (* A285519 *)

%t Flatten[Position[s1, 1]]  (* A285520  *)

%Y Cf. A285504, A285515, A285519, A285520.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 30 2017