A287356 Start with 0 and repeatedly substitute 0->11, 1->12, 2->0.

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

Offset

1,2

Comments

This is the fixed point of the morphism 0->11, 1->12, 2->0 starting with 0. 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 = 5.5707505637226408833903376944272134...,

V = 1.9375648970813894129869852971548390...,

W = 3.2853752818613204416951688472136067....

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 -> {1, 1}, 1 -> {1, 2}, 2 -> 0}] &, {0}, 11] (* A287356 *)
Flatten[Position[s, 0]]  (* A287357 *)
Flatten[Position[s, 1]]  (* A287358 *)
Flatten[Position[s, 2]]  (* A287359 *)

Crossrefs

Cf. A287357, A287358, A287359.

Sequence in context: A358006 A025889 A126306 * A029402 A330443 A268479

Adjacent sequences: A287353 A287354 A287355 * A287357 A287358 A287359

Keyword

nonn,easy

Author

Clark Kimberling, May 24 2017

Status

approved