A285515 - OEIS

%I #5 Apr 30 2017 17:31:43

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

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

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

%N {00->0, 11->1}-transform of A285501.

%C As a word, A285501 = 0011001100110011111100110011111100110011..., so that the transform of A285501 that results from the substitutions 00-> and 11->1 is 01010101110101110101010101011101011101010...  The sequence is also the 0-limiting word of the morphism 0->11, 1->0101.  See A285517 and A285518 for conjectured connections to the golden ratio.

%H Clark Kimberling, <a href="/A285515/b285515.txt">Table of n, a(n) for n = 1..10000</a>

%t s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 0, 1, 1}}] &, {0}, 6] (* A285501 *)

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

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

%t s1 = ToCharacterCode[w1] - 48 (* A285515 *)

%t Flatten[Position[s1, 0]]  (* A285516 *)

%t Flatten[Position[s1, 1]]  (* A285517  *)

%Y Cf. A285501, A285516, A285517, A285518, A285589.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 30 2017