cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A287520 Start with 0 and repeatedly substitute 0->012, 1->102, 2->120.

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%I A287520 #14 Oct 02 2019 21:23:59
%S A287520 0,1,2,1,0,2,1,2,0,1,0,2,0,1,2,1,2,0,1,0,2,1,2,0,0,1,2,1,0,2,0,1,2,1,
%T A287520 2,0,0,1,2,1,0,2,1,2,0,1,0,2,1,2,0,0,1,2,1,0,2,0,1,2,1,2,0,1,0,2,1,2,
%U A287520 0,0,1,2,0,1,2,1,0,2,1,2,0,1,0,2,0,1
%N A287520 Start with 0 and repeatedly substitute 0->012, 1->102, 2->120.
%C A287520 This is the fixed point of the morphism 0->012, 1->102, 2->120 starting with 0.  Let u be the (nonperiodic) sequence of positions of 0, and likewise, v for 1 and w for 2; then u(n)/n -> 3, v(n)/n -> 3,  w(n)/n -> 3.
%C A287520 It is in fact easy to see that |u(n)-3n|<3, |v(n)-3n|<3, and |w(n)-3n|<3. - _Michel Dekking_, Oct 02 2019
%C A287520 See A287385 for a guide to related sequences.
%H A287520 Clark Kimberling, <a href="/A287520/b287520.txt">Table of n, a(n) for n = 1..10000</a>
%H A287520 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%e A287520 First three iterations of the morphism:  012, 012102120, 012102120102012120102120012.
%t A287520 s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 0, 2}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287520*)
%t A287520 Flatten[Position[s, 0]]; (* A287521 *)
%t A287520 Flatten[Position[s, 1]]; (* A287522 *)
%t A287520 Flatten[Position[s, 2]]; (* A189630, conjectured *)
%Y A287520 Cf. A287385, A287521, A287522, A189630.
%K A287520 nonn,easy
%O A287520 1,3
%A A287520 _Clark Kimberling_, May 30 2017