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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
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
Sequence in context: A083913 A363855 A023670 * A188170 A363805 A212193
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 02 2017
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)