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%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
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