A378305 Unique sequence s starting with 2,1,2 such that if r(r(r(s))) = s and r(s) != s and r(r(s)) != s, where r(#) denotes the runlength sequence of a sequence #.

2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1

Offset: 1

Author

Clark Kimberling, Dec 20 2024

Keywords

• nonn

Comments

This sequence is one of three limiting rows of the array A378303. See A378282 for a guide to related arrays and sequences.

Crossrefs

Cf. A378282, A378303, A378304, A378306, A378307.

Programs

Mathematica

z = 18;
invRE[seq_, k_] := Flatten[Map[ConstantArray[#[[2]], #[[1]]] &,
    Partition[Riffle[seq, {k, 2 - Mod[k + 1, 2]}, {2, -1, 2}], 2]]];
row1 = {1}; rows = {row1};
col = PadRight[{}, z, {1, 2, 2}]
Do[AppendTo[rows, invRE[Last[rows], col[[n]]]], {n, 2, Length[col]}]
rows // ColumnForm  (* A378303 *)
rows[[z - 2]];      (* A378304 *)
rows[[z - 1]];      (* A378305 *)
rows[[z]];          (* A378306 *)
Map[Length, rows] (* A378307 *)
(* Peter J. C. Moses, Nov 21 2024 *)