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A286419 {0100->1}-transform of the Thue-Morse word A010060. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 24 00:51 EST 2020. Contains 332195 sequences. (Running on oeis4.)