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A287556 Start with 0 and repeatedly substitute 0->0132, 1->1320, 2->3201, 3->2013. 9
0, 1, 3, 2, 1, 3, 2, 0, 2, 0, 1, 3, 3, 2, 0, 1, 1, 3, 2, 0, 2, 0, 1, 3, 3, 2, 0, 1, 0, 1, 3, 2, 3, 2, 0, 1, 0, 1, 3, 2, 1, 3, 2, 0, 2, 0, 1, 3, 2, 0, 1, 3, 3, 2, 0, 1, 0, 1, 3, 2, 1, 3, 2, 0, 1, 3, 2, 0, 2, 0, 1, 3, 3, 2, 0, 1, 0, 1, 3, 2, 3, 2, 0, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This is the fixed point of the morphism 0->0132, 1->1320, 2->3201, 3->2013 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.

In the following guide to related sequences, column 1 indexes fixed points on {0,1,2,3}, and column 2 indicates position sequences of 0, 1, 2, 3.  Those sequences therefore comprise a 4-way splitting of the positive integers.

Fixed points of morphisms:                        Position sequences:

A053839: 0->0123, 1->1230, 2->2301, 3->3012       A287552-A287555

A287556: 0->0132, 1->1320, 2->3201, 3->2013       A287557-A287560

A287561: 0->0213, 1->2130, 2->1302, 3->3021       A287562-A287565

A287566: 0->0231, 1->2310, 2->3102, 3->1023       A287567-A287570

A287571: 0->0312, 1->3120, 2->1203, 3->2031       A287572-A287575

A287576: 0->0321, 1->3210, 2->2103, 3->1032       A287577-A287580

LINKS

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

Index entries for sequences that are fixed points of mappings

EXAMPLE

First three iterations of the morphism:

0132

0132132020133201

0132132020133201132020133201013232010132132020132013320101321320

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {0, 1, 3, 2}, 1 -> {1, 3, 2, 0}, 2 -> {3, 2, 0, 1}, 3 -> {2, 0, 1, 3}}] &, {0}, 9]; (* A287556 *)

Flatten[Position[s, 0]]; (* A287557 *)

Flatten[Position[s, 1]]; (* A287558 *)

Flatten[Position[s, 2]]; (* A287559 *)

Flatten[Position[s, 3]]; (* A287560 *)

CROSSREFS

Cf. A287557, A287558, A287559, A287560.

Sequence in context: A213514 A130827 A070309 * A236966 A280048 A119910

Adjacent sequences:  A287553 A287554 A287555 * A287557 A287558 A287559

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 31 2017

STATUS

approved

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)