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.
%I A287451 #9 Nov 27 2024 13:03:42 %S A287451 0,1,2,2,0,1,1,2,0,1,2,0,0,1,2,2,0,1,2,0,1,1,2,0,0,1,2,2,0,1,1,2,0,0, %T A287451 1,2,0,1,2,2,0,1,1,2,0,1,2,0,0,1,2,2,0,1,1,2,0,0,1,2,2,0,1,2,0,1,1,2, %U A287451 0,0,1,2,0,1,2,2,0,1,1,2,0,1,2,0,0,1 %N A287451 Start with 0 and repeatedly substitute 0->012, 1->201, 2->120. %C A287451 This is the fixed point of the morphism 0->012, 1->201, 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 A287451 See A287385 for a guide to related sequences. %H A287451 Clark Kimberling, <a href="/A287451/b287451.txt">Table of n, a(n) for n = 1..10000</a> %H A287451 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a> %e A287451 First three iterations of the morphism: 012, 012201120, 012201120120012201201120012. %t A287451 s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 0, 1}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287451*) %t A287451 Flatten[Position[s, 0]]; (*A287452*) %t A287451 Flatten[Position[s, 1]]; (*A287453*) %t A287451 Flatten[Position[s, 2]]; (*A287454*) %t A287451 SubstitutionSystem[{0->{0,1,2},1->{2,0,1},2->{1,2,0}},{0},{5}][[1]] (* _Harvey P. Dale_, Nov 27 2024 *) %Y A287451 Cf. A287385, A287452, A287453, A287454. %K A287451 nonn,easy %O A287451 1,3 %A A287451 _Clark Kimberling_, May 30 2017