This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A249942 #15 Nov 22 2017 01:15:05
%S A249942 7,10,20,25,34,37,43,46,55,61,64,73,76,82,88,91,101,106,109,118,128,
%T A249942 137,143,146,152,155,164,170,173,182,187,196,199,205,211,214,223,233,
%U A249942 236,241,251,260,263,268,277,280,286,289,298,301,307,313,316,326,331,334
%N A249942 Ranks of single 1's in the Kolakoski sequence A000002.
%C A249942 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.
%C A249942 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).
%C A249942 A249948 gives the gaps between single 1's.
%H A249942 Jean-Christophe Hervé, <a href="/A249942/b249942.txt">Table of n, a(n) for n = 1..10000</a>
%F A249942 a = {A054353(2k+1), k>1 and A000002(2k+1) = 1}.
%F A249942 Odd values of A216345: A216345(2k+1), k>0, such that A216345(2k+2) =
%F A249942 A216345(2k+1)+1.
%Y A249942 A000002, A054351, A054352, A249093, A249094, A249507, A249508, A249948, A249949.
%K A249942 nonn
%O A249942 1,1
%A A249942 _Jean-Christophe Hervé_, Nov 08 2014