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%I #4 May 31 2017 21:24:58
%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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