A286053 - OEIS

%I #4 May 07 2017 21:36:18

%S 1,3,4,5,8,9,10,11,12,13,14,16,17,19,20,21,24,25,26,28,29,31,32,33,34,

%T 35,36,37,40,41,42,43,44,45,46,48,49,51,52,53,54,55,56,57,60,61,62,64,

%U 65,67,68,69,72,73,74,75,76,77,78,80,81,83,84,85,88,89

%N Positions of 0 in A286052; complement of A286054.

%C Conjecture: a(n)/n -> 4/3.

%H Clark Kimberling, <a href="/A286053/b286053.txt">Table of n, a(n) for n = 1..10000</a>

%e As a word, A286052 = 01000110000000100100..., in which 0 is in positions 1,3,4,5,3,...

%t s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* Thue-Morse, A010060 *)

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

%t w1 = StringReplace[w, {"101" -> "0"}]

%t st = ToCharacterCode[w1] - 48 (* A286052 *)

%t Flatten[Position[st, 0]]  (* A286053 *)

%t Flatten[Position[st, 1]]  (* A286054 *)

%Y Cf. A010060, A286052, A286054.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, May 07 2017