A342799 Numbers m such that there are more 1s than 2s in {K(1), .., K(m)}, where K = A000002 (Kolakoski sequence).

1, 5, 7, 17, 23, 25, 29, 31, 32, 33, 34, 35, 37, 41, 43, 49, 51, 52, 53, 55, 59, 61, 71, 73, 79, 125, 131, 133, 134, 135, 137, 141, 143, 149, 161, 179, 185, 187, 191, 193, 194, 195, 196, 197, 199, 201, 202, 203, 205, 209, 211, 221, 223, 227, 229, 230, 231

Offset: 1

Author

Clark Kimberling, May 10 2021

Keywords

• nonn

Comments

The three sequences A022292 (without the initial 0), A074261, and A342799 partition the positive integers.

Examples

			The Kolakoski sequence is (1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, ...), so that a(1) = 1, a(2) = 5.
		

Crossrefs

Cf. A000002, A022292, A022293, A074261.

Programs

Mathematica

k = Prepend[Nest[Flatten[Partition[#, 2] /. {{2, 2} -> {2, 2, 1, 1}, {2, 1} -> {2, 2, 1}, {1, 2} -> {2, 1, 1}, {1, 1} -> {2, 1}}] &, {2, 2}, 14], 1]; (* A000002 *)
Select[Range[400], Count[Take[k, #], 1] < #/2 &]   (* A074261 *)
Select[Range[400], Count[Take[k, #], 1] == #/2 &]  (* A022292 *)
Select[Range[400], Count[Take[k, #], 1] > #/2 &]   (* A342799 *)