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.

A287401 Start with 0 and repeatedly substitute 0->012, 1->210, 2->120.

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%I A287401 #11 Jul 11 2022 13:44:15
%S A287401 0,1,2,2,1,0,1,2,0,1,2,0,2,1,0,0,1,2,2,1,0,1,2,0,0,1,2,2,1,0,1,2,0,0,
%T A287401 1,2,1,2,0,2,1,0,0,1,2,0,1,2,2,1,0,1,2,0,1,2,0,2,1,0,0,1,2,2,1,0,1,2,
%U A287401 0,0,1,2,0,1,2,2,1,0,1,2,0,1,2,0,2,1
%N A287401 Start with 0 and repeatedly substitute 0->012, 1->210, 2->120.
%C A287401 This is the fixed point of the morphism 0->012, 1->210, 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 A287401 See A287385 for a guide to related sequences.
%H A287401 Clark Kimberling, <a href="/A287401/b287401.txt">Table of n, a(n) for n = 1..10000</a>
%H A287401 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%F A287401 a(n) = (2*a(m) + (n-1)*(-1)^a(m)) mod 3, where m = 1 + floor((n-1)/3). - _Max Alekseyev_, Jul 11 2022
%e A287401 First three iterations of the morphism:  012, 012210102, 012210102102210012210012102.
%t A287401 s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 1, 0}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287401*)
%t A287401 Flatten[Position[s, 0]]; (*A189728*)
%t A287401 Flatten[Position[s, 1]]; (*A287403*)
%t A287401 Flatten[Position[s, 2]]; (*A287404*)
%Y A287401 Cf. A189728, A287385, A287403, A287404.
%K A287401 nonn,easy
%O A287401 1,3
%A A287401 _Clark Kimberling_, May 25 2017