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A287571 Start with 0 and repeatedly substitute 0->0312, 1->3120, 2->1203, 3->2031. 6

%I

%S 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,

%T 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,

%U 1,2,0,3,0,3,1,2,2,0,3,1,0,3,1,2,2,0

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

%C 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.

%H Clark Kimberling, <a href="/A287571/b287571.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

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

%e First three iterations of the morphism:

%e 0312

%e 0312203131201203

%e 0312203131201203120303122031312020313120120303123120120303122031

%t 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 *)

%t Flatten[Position[s, 0]]; (* A287572 *)

%t Flatten[Position[s, 1]]; (* A287573 *)

%t Flatten[Position[s, 2]]; (* A287574 *)

%t Flatten[Position[s, 3]]; (* A287575 *)

%Y Cf. A287572, A287573, A287574, A287575.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, May 31 2017

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Last modified June 20 13:53 EDT 2021. Contains 345165 sequences. (Running on oeis4.)