A286044 {011->0}-transform of the Thue-Morse word A010060.

0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0

Offset

1

Comments

This is also the {110->1}-transform of A010060.

Links

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

Formula

Conjecture: a(n) = b(b(n - 2)) - b(b(n - 3)) for n > 3, where b is A003160. - Velin Yanev, Feb 16 2026

Example

As a word, A010060 = 0110100110010110100101100..., and replacing each 011 by 0 gives 00100001001001000010000100001...

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 *)
Most[SequenceReplace[Array[ThueMorse, 2^9, 0], {0, 1, 1} -> 0]] (* Velin Yanev, Feb 16 2026 *)

Crossrefs

Cf. A010060, A286045, A003157.

Sequence in context: A305388 A123740 A188472 * A129272 A059648 A288707

Adjacent sequences: A286041 A286042 A286043 * A286045 A286046 A286047

Keyword

nonn,easy

Author

Clark Kimberling, May 07 2017

Status

approved