A249942 Ranks of single 1's in the Kolakoski sequence A000002.

7, 10, 20, 25, 34, 37, 43, 46, 55, 61, 64, 73, 76, 82, 88, 91, 101, 106, 109, 118, 128, 137, 143, 146, 152, 155, 164, 170, 173, 182, 187, 196, 199, 205, 211, 214, 223, 233, 236, 241, 251, 260, 263, 268, 277, 280, 286, 289, 298, 301, 307, 313, 316, 326, 331, 334

Offset

1,1

Comments

The single 1's whose ranks are given by this sequence are the 1's between two 2's in the OK sequence A000002. They are associated with iterated words of the OK sequence that develop themselves around each single 1 in two branches (for a description of the iterated words, see comments in A249507, which gives their lengths). The first term of A000002, which is indeed a single 1 but not between two 2's, is thus not considered here.

Each such single 1 is generated by a preceding 1 in the OK sequence that could be single or double, but each single 1 has a double 1 in its ancestors since the first 1 of the OK sequence has no descendants except itself. The length of the iterated word around a single 1 is linked to the number of generations between itself and its nearest double 1 ancestor (A249949 gives the number of generations of the n-th single 1).

A249948 gives the gaps between single 1's.

Links

Jean-Christophe Hervé, Table of n, a(n) for n = 1..10000

Formula

a = {A054353(2k+1), k>1 and A000002(2k+1) = 1}.

Odd values of A216345: A216345(2k+1), k>0, such that A216345(2k+2) =

A216345(2k+1)+1.

Crossrefs

A000002, A054351, A054352, A249093, A249094, A249507, A249508, A249948, A249949.

Sequence in context: A122226 A240791 A064210 * A300021 A363292 A327977

Adjacent sequences: A249939 A249940 A249941 * A249943 A249944 A249945

Keyword

nonn

Author

Jean-Christophe Hervé, Nov 08 2014

Status

approved