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A287524 Start with 0 and repeatedly substitute 0->012, 1->102, 2->201. 3
0, 1, 2, 1, 0, 2, 2, 0, 1, 1, 0, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 0, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 2, 2, 0, 1, 0, 1, 2, 1, 0, 2, 2, 0, 1, 2, 0, 1, 0, 1, 2, 1, 0, 2, 2, 0, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 2, 0, 1, 1, 0, 2, 0, 1, 2, 2, 0, 1, 1, 0, 2, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This is the fixed point of the morphism 0->012, 1->102, 2->201 starting with 0.  Let u be the (nonperiodic) sequence of positions of 0, and likewise, v for 1 and w for 2; then u(n)/n -> 3, v(n)/n -> 3,  w(n)/n -> 3.

See A287385 for a guide to related sequences.

LINKS

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

Index entries for sequences that are fixed points of mappings

EXAMPLE

First three iterations of the morphism:  012, 012102201, 012102201102012201201012102.

MATHEMATICA

s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 0, 2}, 2->{2, 0, 1}}] &, {0}, 9]; (*A287524*)

Flatten[Position[s, 0]]; (*A189724*)

Flatten[Position[s, 1]]; (*A287526*)

Flatten[Position[s, 2]]; (*A189634*)

CROSSREFS

Cf. A189724, A287385, A287526, A189634.

Sequence in context: A258279 A258292 A003985 * A157237 A065676 A281461

Adjacent sequences:  A287521 A287522 A287523 * A287525 A287526 A287527

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 30 2017

STATUS

approved

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Last modified October 17 10:50 EDT 2017. Contains 293469 sequences.