A381848 -id:A381848 - cp's OEIS frontend

A383999 Sequence obtained by replacing 3-term subwords of A003849 by 0,1,2,3 as described in Comments.

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, 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, 1, 2, 0, 1, 3, 1, 2, 0, 1, 2, 0, 1, 3, 1, 2, 0, 1, 2

Offset: 1

Clark Kimberling, May 23 2025

nonn

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.

			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,... .

Cf. A003849, A003623, A003622, A035336, A101864, A035513, A381848.

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 *)

cp's OEIS Frontend

A383999 Sequence obtained by replacing 3-term subwords of A003849 by 0,1,2,3 as described in Comments.

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