A287418 Start with 0 and repeatedly substitute 0->012, 1->120, 2->102.

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

Offset: 1

Author

Clark Kimberling, May 25 2017

Keywords

• nonn
• easy

Comments

This is the fixed point of the morphism 0->012, 1->120, 2->102 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, 012120102, 012120102120102012120012102.
		

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, A287419, A287420, A287421.

Programs

Mathematica

s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 2, 0}, 2->{1, 0, 2}}] &, {0}, 9]; (*A287418*)
Flatten[Position[s, 0]]; (*A287419*)
Flatten[Position[s, 1]]; (*A287420*)
Flatten[Position[s, 2]]; (*A287421*)
SubstitutionSystem[{0->{0,1,2},1->{1,2,0},2->{1,0,2}},{0},{5}][[1]] (* Harvey P. Dale, Oct 09 2023 *)