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A287561 Start with 0 and repeatedly substitute 0->0213, 1->2130, 2->1302, 3->3021. 6
0, 2, 1, 3, 1, 3, 0, 2, 2, 1, 3, 0, 3, 0, 2, 1, 2, 1, 3, 0, 3, 0, 2, 1, 0, 2, 1, 3, 1, 3, 0, 2, 1, 3, 0, 2, 2, 1, 3, 0, 3, 0, 2, 1, 0, 2, 1, 3, 3, 0, 2, 1, 0, 2, 1, 3, 1, 3, 0, 2, 2, 1, 3, 0, 1, 3, 0, 2, 2, 1, 3, 0, 3, 0, 2, 1, 0, 2, 1, 3, 3, 0, 2, 1, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is the fixed point of the morphism 0->0213, 1->2130, 2->1302, 3->3021 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 - A287565(n) for n >= 1.

EXAMPLE

First three iterations of the morphism:

0213

0213130221303021

0213130221303021213030210213130213022130302102133021021313022130

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {0, 2, 1, 3}, 1 -> {2, 1, 3, 0}, 2 -> {1, 3, 0, 2}, 3 -> {3, 0, 2, 1}}] &, {0}, 9];   (* A287561 *)

Flatten[Position[s, 0]]; (* A287562 *)

Flatten[Position[s, 1]]; (* A287563 *)

Flatten[Position[s, 2]]; (* A287564 *)

Flatten[Position[s, 3]]; (* A287565 *)

CROSSREFS

Cf. A287562, A287563, A287564, A287565.

Sequence in context: A293980 A240694 A258643 * A046924 A015710 A108415

Adjacent sequences:  A287558 A287559 A287560 * A287562 A287563 A287564

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 31 2017

STATUS

approved

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Last modified November 21 22:40 EST 2019. Contains 329383 sequences. (Running on oeis4.)