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A284394 {101->2}-transform of the infinite Fibonacci word A003849. 3
0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The sequences p = A032766, q = A284395, r = A284396, of positions of 0,1,2, respectively, partition the positive integers.  Let t,u,v be the slopes of p, q, r, respectively.  Then t = 3/2, u = (9+3*sqrt(5))/2, v = (3+3*sqrt(5))/2, and 1/t + 1/u + 1/v = 1.

LINKS

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

EXAMPLE

As a word, A003849 = 01001010010010100..., and replacing each 101 by 2 gives 01002001002002001...

MATHEMATICA

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

w = StringJoin[Map[ToString, s]]; w1 = StringReplace[w, {"101" -> "2"}]

st = ToCharacterCode[w1] - 48 (* A284394 *)

Flatten[Position[st, 0]]  (* A032766 *)

Flatten[Position[st, 1]]  (* A284395 *)

Flatten[Position[st, 2]]  (* A284396 *)

CROSSREFS

Cf. A003849, A032766, A284395, A284396.

Sequence in context: A103612 A083913 A023670 * A188170 A212193 A253189

Adjacent sequences:  A284391 A284392 A284393 * A284395 A284396 A284397

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 02 2017

STATUS

approved

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Last modified June 13 20:25 EDT 2021. Contains 345009 sequences. (Running on oeis4.)