A287773 {0->010, 1->101}-transform of the infinite Fibonacci word A003849.

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

Offset

1

Links

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

Formula

a(n) = 1 - A287795(n) for n >= 1.

Example

As a word, A003849 = 0100101001001010010100100..., and replacing each 0 by 010 and each 1 by 101 gives 01010101001010101010101001010101001...

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 10] (* A003849 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0" -> "010", "1" -> "101"}]
st = ToCharacterCode[w1] - 48    (* A287773 *)
Flatten[Position[st, 0]]  (* A287774 *)
Flatten[Position[st, 1]]  (* A287777 *)

Crossrefs

Cf. A287774, A287777; A287795 (binary complement).

Sequence in context: A139312 A323239 A285685 * A173923 A260393 A360113

Adjacent sequences: A287770 A287771 A287772 * A287774 A287775 A287776

Keyword

nonn,easy

Author

Clark Kimberling, Jun 03 2017

Status

approved