

A249942


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


4



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
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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 nth single 1).
A249948 gives the gaps between single 1's.


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CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



