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A287571 Start with 0 and repeatedly substitute 0->0312, 1->3120, 2->1203, 3->2031. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..20000

Index entries for sequences that are fixed points of mappings

FORMULA

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

EXAMPLE

First three iterations of the morphism:

0312

0312203131201203

0312203131201203120303122031312020313120120303123120120303122031

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 *)

CROSSREFS

Cf. A287572, A287573, A287574, A287575.

Sequence in context: A070773 A046804 A263211 * A214316 A236452 A056529

Adjacent sequences:  A287568 A287569 A287570 * A287572 A287573 A287574

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 31 2017

STATUS

approved

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Last modified October 20 17:39 EDT 2017. Contains 293648 sequences.