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A342799
Numbers m such that there are more 1s than 2s in {K(1), .., K(m)}, where K = A000002 (Kolakoski sequence).
3
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.
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 10 2021
STATUS
approved