A287571 Start with 0 and repeatedly substitute 0->0312, 1->3120, 2->1203, 3->2031.

0, 3, 1, 2, 2, 0, 3, 1, 3, 1, 2, 0, 1, 2, 0, 3, 1, 2, 0, 3, 0, 3, 1, 2, 2, 0, 3, 1, 3, 1, 2, 0, 2, 0, 3, 1, 3, 1, 2, 0, 1, 2, 0, 3, 0, 3, 1, 2, 3, 1, 2, 0, 1, 2, 0, 3, 0, 3, 1, 2, 2, 0, 3, 1, 3, 1, 2, 0, 1, 2, 0, 3, 0, 3, 1, 2, 2, 0, 3, 1, 0, 3, 1, 2, 2, 0

Offset: 1

Author

Clark Kimberling, May 31 2017

Keywords

• nonn
• easy

Comments

This is the fixed point of the morphism 0->0231, 1->2310, 2->3102, 3->1023 starting with 0. Let t be the (nonperiodic) sequence of positions of 0, and likewise, u for 1, v for 2, and w for 3; then t(n)/n -> 4, u(n)/n -> 4, v(n)/n -> 4, w(n)/n -> 4. Also, t(n) + u(n) + v(n) + w(n) = 16*n - 6 for n >= 1. See A287556 for a guide to related sequences.

Examples

			First three iterations of the morphism:
0312
0312203131201203
0312203131201203120303122031312020313120120303123120120303122031
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..20000
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A287572, A287573, A287574, A287575.

Programs

Mathematica

s = Nest[Flatten[# /. {0 -> {0,3,1,2}, 1 -> {3,1,2,0}, 2 -> {1,2,0,3}, 3 -> {2,0,3,1}}] &, {0}, 9];   (* A287571 *)
Flatten[Position[s, 0]]; (* A287572 *)
Flatten[Position[s, 1]]; (* A287573 *)
Flatten[Position[s, 2]]; (* A287574 *)
Flatten[Position[s, 3]]; (* A287575 *)

Formula

a(n) = 4n - A287574(n) for n >= 1.