

A284388


0limiting 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
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OFFSET

1


COMMENTS

The morphism 0 > 1, 1 > 001 has two limiting words. If the number of iterations is even, the 0word evolves from 0 > 1 > 001 > 11001 > 00100111001; if the number of iterations is odd, the 1word evolves from 0 > 1 > 001 > 11001 > 00100111001 > 110011100100100111001, as in A284391. The 0limiting 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 runlengths of the ThueMorse 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



