A286045 Positions of 0 in A286044; complement of A003157.

1, 2, 4, 5, 6, 7, 9, 10, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 28, 30, 31, 33, 34, 36, 37, 38, 39, 41, 42, 44, 45, 47, 48, 49, 50, 52, 53, 55, 56, 58, 59, 60, 61, 63, 64, 65, 66, 68, 69, 70, 71, 73, 74, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87

Offset: 1

Author

Clark Kimberling, May 07 2017

Keywords

• nonn
• easy

Comments

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

Also, these are the positions of 0 in the {110->1}-transform of A010060.

Examples

			As a word, A286044 = 001000010010010000100..., in which 0 is in positions 1,2,4,5,6,7,9,...
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010060, A286044, A003157.

Programs

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* Thue-Morse, A010060 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"011" -> "0"}]
st = ToCharacterCode[w1] - 48 (* A286044 *)
Flatten[Position[st, 0]]  (* A286045 *)
Flatten[Position[st, 1]]  (* A003157 *)