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A284749 {001->2}-transform of the infinite Fibonacci word A003849. 6
0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

From Dan Rust, Aug 18 2018: (Start)

This word is the fixed point of the morphism 0->2, 1->01, 2->2201 with the finite string 0, 1, 2, 0, 1 appended to the beginning. This morphism comes from taking the 'proper' version of the Fibonacci morphism 0->01, 1->1, given by 0->001, 1->01 (A189661 but with the rightmost 0 moved to the left of each image word), then replacing 001 with 2 and noting that the new symbol 2 should map to 00100101 = 2201 in order to be consistent.

The finite string appended to the beginning comes from the process of finding a proper version of the Fibonacci morphism using a return word encoding and taking conjugates which causes a shift of the respective fixed points.

(End)

This sequence is the unique fixed point of the morphism 0->01, 1->2, 2->0122. See the paragraph following Lemma 23 in the paper by Allouche and myself. - Michel Dekking, Oct 05 2018

LINKS

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

J.-P. Allouche, F. M. Dekking, Generalized Beatty sequences and complementary triples, arXiv:1809.03424v3 [math.NT], 2018-2019.

EXAMPLE

As a word, A003849 = 01001010010010100..., and replacing each 001 by 2 gives 01201220120...

MATHEMATICA

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

w = StringJoin[Map[ToString, s]]

w1 = StringReplace[w, {"001" -> "2"}]

st = ToCharacterCode[w1] - 48 (* A284749 *)

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

Flatten[Position[st, 1]]  (* A284624 *)

Flatten[Position[st, 2]]  (* A284625 *)

CROSSREFS

Cf. A003849, A214971, A284624, A284625.

Sequence in context: A248806 A118407 A101663 * A062169 A113680 A316723

Adjacent sequences:  A284746 A284747 A284748 * A284750 A284751 A284752

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 02 2017

STATUS

approved

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)