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 A383999 #6 May 29 2025 00:34:26
%S A383999 1,2,0,1,3,1,2,0,1,2,0,1,3,1,2,0,1,3,1,2,0,1,2,0,1,3,1,2,0,1,2,0,1,3,
%T A383999 1,2,0,1,3,1,2,0,1,2,0,1,3,1,2,0,1,3,1,2,0,1,2,0,1,3,1,2,0,1,2,0,1,3,
%U A383999 1,2,0,1,3,1,2,0,1,2,0,1,3,1,2,0,1,2
%N A383999 Sequence obtained by replacing 3-term subwords of A003849 by 0,1,2,3 as described in Comments.
%C A383999 The four 3-term subwords of A003849 are 0,0,1; 0,1,0; 1,0,0; 1,0,1. These are coded as 0,1,2,3, respectively, and then these numbers replace the corresponding subwords in A003849. In the resulting sequence, the positions of 0,1,2,3 are given by A003623, A003622, A035336, A101864, which are the x-Wythoff sequences for x = AB, AA, BA, BB, respectively. The corresponding limiting densities are sqrt(5)-2, (3-sqrt(5))/2, sqrt(5)-2, (7-3*sqrt(5))/2.
%e A383999 Starting with A003849 = (0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,...), the successive 3-term subwords are 0,1,0; 1,0,0; 0,0,1; 0,1,0; 1,0,1; ..., which code as 1,2,0,1,3,... .
%t A383999 Partition[Nest[Flatten[#/. {0->{0,1},1->{0}}]&,{0},10],3,1]/.Thread[{{0,0,1},{0,1,0},{1,0,0},{1,0,1}}->{0,1,2,3}] (* _Peter J. C. Moses_, May 22 2025 *)
%Y A383999 Cf. A003849, A003623, A003622, A035336, A101864, A035513, A381848.
%K A383999 nonn
%O A383999 1,2
%A A383999 _Clark Kimberling_, May 23 2025