A287451 Start with 0 and repeatedly substitute 0->012, 1->201, 2->120.

0, 1, 2, 2, 0, 1, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 0, 1, 2, 0, 1, 1, 2, 0, 0, 1, 2, 2, 0, 1, 1, 2, 0, 0, 1, 2, 0, 1, 2, 2, 0, 1, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 0, 1, 1, 2, 0, 0, 1, 2, 2, 0, 1, 2, 0, 1, 1, 2, 0, 0, 1, 2, 0, 1, 2, 2, 0, 1, 1, 2, 0, 1, 2, 0, 0, 1

Offset

1,3

Comments

This is the fixed point of the morphism 0->012, 1->201, 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, 012201120, 012201120120012201201120012.

Mathematica

s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 0, 1}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287451*)
Flatten[Position[s, 0]]; (*A287452*)
Flatten[Position[s, 1]]; (*A287453*)
Flatten[Position[s, 2]]; (*A287454*)
SubstitutionSystem[{0->{0, 1, 2}, 1->{2, 0, 1}, 2->{1, 2, 0}}, {0}, {5}][[1]] (* Harvey P. Dale, Nov 27 2024 *)

Crossrefs

Cf. A287385, A287452, A287453, A287454.

Sequence in context: A156311 A270740 A189463 * A113414 A286653 A283308

Adjacent sequences: A287448 A287449 A287450 * A287452 A287453 A287454

Keyword

nonn,easy

Author

Clark Kimberling, May 30 2017

Status

approved