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A287520 Start with 0 and repeatedly substitute 0->012, 1->102, 2->120. 4
0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 2, 0, 1, 0, 2, 1, 2, 0, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 2, 0, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 1, 2, 0, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 2, 0, 1, 0, 2, 1, 2, 0, 0, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 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->120 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, 012102120, 012102120102012120102120012.

MATHEMATICA

s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 0, 2}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287520*)

Flatten[Position[s, 0]]; (*A287521*)

Flatten[Position[s, 1]]; (*A287522*)

Flatten[Position[s, 2]]; (*A189630*)

CROSSREFS

Cf. A287385, A287521, A287522, A189630.

Sequence in context: A029295 A185204 A217522 * A130094 A230025 A207869

Adjacent sequences:  A287517 A287518 A287519 * A287521 A287522 A287523

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 30 2017

STATUS

approved

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Last modified November 24 00:27 EST 2017. Contains 295164 sequences.