A378283 Unique sequence s starting with 1,1,2,1 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 #.

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

Offset: 1

Author

Clark Kimberling, Dec 16 2024

Keywords

• nonn

Comments

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

Crossrefs

Cf. A378282, A378284, A378285, A378286, A378303.

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, 1, 2}]
Do[AppendTo[rows, invRE[Last[rows], col[[n]]]], {n, 2, Length[col]}]
rows // ColumnForm
Flatten[rows]   (* A378282 *)
rows[[z - 2]];  (* A378283 *)
rows[[z - 1]];  (* A378284 *)
rows[[z]];      (* A378285 *)
Map[Length, rows]   (* A378286 *)
(* Peter J. C. Moses, Nov 21 2024 *)