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A284388 0-limiting word of the morphism 0 -> 1, 1 -> 001. 4
0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

The morphism 0 -> 1, 1 -> 001 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 1 -> 001 -> 11001 -> 00100111001; if the number of iterations is odd, the 1-word evolves from 0 -> 1 -> 001 -> 11001 -> 00100111001 -> 110011100100100111001, as in A284391. The 0-limiting word results from the 1 limiting word by replacing the initial 00 by 1.

Conjecture: the limiting frequency of 0's in both limiting words is 1/2.

Conjecture: after the first term, same as one less than the run-lengths of the Thue-Morse sequence A010060. - George Beck, Mar 24 2021

LINKS

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

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {0, 0, 1}}] &, {0}, 8]; (* A284388 *)

Flatten[Position[s, 0]];  (* A284389 *)

Flatten[Position[s, 1]];  (* A284390 *)

CROSSREFS

Cf. A010060, A284389, A284390, A284391.

Sequence in context: A273129 A288936 A064990 * A289174 A059125 A189820

Adjacent sequences:  A284385 A284386 A284387 * A284389 A284390 A284391

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 30 2017

STATUS

approved

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Last modified August 5 07:02 EDT 2021. Contains 346458 sequences. (Running on oeis4.)