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

1,2

Comments

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

Links

Table of n, a(n) for n=1..57.

Example

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.

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 *)

Crossrefs

Cf. A000002, A022292, A022293, A074261.

Sequence in context: A331893 A331895 A164120 * A043879 A370855 A044966

Adjacent sequences: A342796 A342797 A342798 * A342800 A342801 A342802

Keyword

nonn

Author

Clark Kimberling, May 10 2021

Status

approved