A284394 {101->2}-transform of the infinite Fibonacci word A003849.

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

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: A083913 A363855 A023670 * A188170 A363805 A212193

Adjacent sequences: A284391 A284392 A284393 * A284395 A284396 A284397

Keyword

nonn,easy

Author

Clark Kimberling, May 02 2017

Status

approved