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A284387 {010->2}-transform of the infinite Fibonacci word A003849. 1
2, 2, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequences p = A214971, q = A003231, r = A276886 of positions of 0, 1, 2, respectively.  Let t,u,v be the slopes of p, q, r, respectively.  Then t = (5+sqrt(5))/2, u = (5+sqrt(5))/2, v = sqrt(5), and 1/t + 1/u + 1/v = 1.  If 1 is removed from p (or from r), the resulting three sequences partition the set of positive integers.

LINKS

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

EXAMPLE

As a word, A003849 = 01001010010010100..., and replacing each 010 by 2 gives 2210221021...

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13]  (* A003849 *)

w = StringJoin[Map[ToString, s]]

w1 = StringReplace[w, {"010" -> "2"}]

st = ToCharacterCode[w1] - 48 (* A284387 *)

Flatten[Position[st, 0]]  (* A214971 *)

Flatten[Position[st, 1]]  (* A003231 *)

Flatten[Position[st, 2]]  (* A276886 *)

CROSSREFS

Cf. A003231, A003849, A214971, A276886.

Sequence in context: A001617 A282947 A287200 * A143667 A246785 A084934

Adjacent sequences:  A284384 A284385 A284386 * A284388 A284389 A284390

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 02 2017

EXTENSIONS

Comment edited by Clark Kimberling, Oct 14 2017

STATUS

approved

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Last modified February 24 07:50 EST 2018. Contains 299599 sequences. (Running on oeis4.)