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 A026609 #13 Apr 15 2019 07:27:43 %S A026609 2,1,1,1,0,2,0,2,1,1,0,2,0,2,0,2,1,1,0,2,0,2,1,1,1,0,2,1,0,2,0,2,0,2, %T A026609 1,1,0,2,0,2,1,1,1,0,1,2,1,1,1,0,2,0,2,1,0,2,0,2,1,1,1,0,1,2,1,1,1,0, %U A026609 2,0,2,1,1,0,2,0,2,0,2,1,1,1,0,2,0,2,0,2,1,1 %N A026609 a(n) = number of 3's between n-th 1 and (n+1)st 1 in A026600. %C A026609 From _Michel Dekking_, Apr 15 2019: (Start) %C A026609 (a(n)) is a morphic sequence, i.e., a letter-to-letter projection of a fixed point of a morphism. This follows from a study of the return words of 1 in (a(n)): the word 1 in (a(n)) has 7 return words. These are A:=1, B:=123, C:=12, D:=13, E:=12323, F:=1233, G:=1223. %C A026609 The sequence A026600 is fixed point of the 3-symbol Thue-Morse morphism mu given by mu: 1->123, 2->231, 3->312. %C A026609 This induces a morphism beta on the return words given by beta: A->B, B->EDC, C->EA, D->FC, E->EDGDC, F->EDBC, G->EBDC. %C A026609 Counting 3's in the return words yields the morphism gamma given by gamma: A->0, B->1, C->0, D->1, E->2, F->2, G->1. %C A026609 Let y = EDGDCFCEBDCFC... be the unique fixed point of beta. Then clearly (a(n)) = gamma(y). %C A026609 (End) %C A026609 The frequencies of 0's, 1's and 2's in (a(n)) are 4/13, 5/13 and 4/13. - _Michel Dekking_, Apr 15 2019 %e A026609 beta(B) = mu(123) = 123231312 = EDC. %K A026609 nonn %O A026609 1,1 %A A026609 _Clark Kimberling_