A286050 - OEIS

%I #4 May 07 2017 21:35:58

%S 1,4,5,7,9,12,13,15,17,20,21,23,25,27,30,31,33,36,37,39,41,44,45,47,

%T 49,52,53,55,58,59,61,63,65,68,69,71,73,76,77,79,81,84,85,87,89,91,94,

%U 95,97,100,101,103,105,107,110,111,113,115,118,119,121,123

%N Positions of 0 in A286049; complement of A286051.

%C Conjecture: 2n - a(n) is in {0,1} for n >= 1.

%C Also, the positions of 0 in the {100->0}-transform of A010060.

%H Clark Kimberling, <a href="/A286050/b286050.txt">Table of n, a(n) for n = 1..10000</a>

%e As a word, A286049 = 0110010101100101..., in which 0 is in positions 1,4,5,7,9,...

%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, {"110" -> "1"}]

%t st = ToCharacterCode[w1] - 48 (* A286049 *)

%t Flatten[Position[st, 0]]  (* A286050 *)

%t Flatten[Position[st, 1]]  (* A286051 *)

%Y Cf. A010060, A286049, A286051.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, May 07 2017