A286419 {0100->1}-transform of the Thue-Morse word A010060.

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

Offset

1

Comments

Let u(n) be the initial (2^n)-letter subword of A010060, and let v(n) be the word remaining when {0100->1} is applied to u(n). Then for n>=2, |v(n)| = 3*2^(n-2) - 1 if n is odd, and |v(n)| = 3*2^(n-2)+1 if n is even.

Links

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

Example

As a word, A010060 = 0110100110010110100101100..., and replacing each 0100 by 1 gives 0111110010111101100111110010...

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* A010060 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0100" -> "1"}]
st = ToCharacterCode[w1] - 48  (* A286419 *)
Flatten[Position[st, 0]]  (* A286420 *)
Flatten[Position[st, 1]]  (* A286421 *)

Crossrefs

Cf. A010060, A286420, A286421.

Sequence in context: A143536 A204437 A080110 * A257799 A089496 A182067

Adjacent sequences: A286416 A286417 A286418 * A286420 A286421 A286422

Keyword

nonn,easy

Author

Clark Kimberling, May 09 2017

Status

approved