A287002 Start with 0 and repeatedly substitute 0->01, 1->20, 2->1.

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

Offset

1,3

Comments

A fixed point of the morphism 0->01, 1->20, 2->1. Let u be the sequence of positions of 0, and likewise, v for 1 and w for 2. Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively. Then 1/U + 1/V + 1/W = 1, where

U = 2.246979603717467061050009768008...,

V = 2.801937735804838252472204639014...,

W = 5.048917339522305313522214407023...

If n >=2, then u(n) - u(n-1) is in {1,2,3}, v(n) - v(n-1) is in {2,3,4}, and w(n) - w(n-1) is in {4,5,7}.

Links

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

Index entries for sequences that are fixed points of mappings

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {2, 0}, 2 -> 1}] &, {0}, 10] (* A287002 *)
Flatten[Position[s, 0]]  (* A287003 *)
Flatten[Position[s, 1]]  (* A287004 *)
Flatten[Position[s, 2]]  (* A287081 *)
SubstitutionSystem[{0->{0, 1}, 1->{2, 0}, 2->{1}}, {0}, {10}][[1]] (* Harvey P. Dale, Feb 27 2023 *)

Crossrefs

Cf. A287003, A287004, A287081.

Sequence in context: A132343 A277731 A298307 * A119346 A014586 A122924

Adjacent sequences: A286999 A287000 A287001 * A287003 A287004 A287005

Keyword

nonn,easy

Author

Clark Kimberling, May 21 2017

Status

approved