A287516 Start with 0 and repeatedly substitute 0->012, 1->102, 2->021.

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

Offset: 1

Author

Clark Kimberling, May 30 2017

Keywords

• nonn
• easy

Comments

This is the fixed point of the morphism 0->012, 1->102, 2->021 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.

Examples

			First three iterations of the morphism:  012, 012102021, 012102021102012021012021102.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A287385, A287517, A287518, A287519.

Programs

Mathematica

s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 0, 2}, 2->{0, 2, 1}}] &, {0}, 9]; (*A287516*)
Flatten[Position[s, 0]]; (*A287517*)
Flatten[Position[s, 1]]; (*A287518*)
Flatten[Position[s, 2]]; (*A287519*)
SubstitutionSystem[{0->{0,1,2},1->{1,0,2},2->{0,2,1}},{0},{5}][[1]] (* Harvey P. Dale, Dec 22 2024 *)