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 A282198 #14 Feb 10 2017 01:13:57
%S A282198 1,3,11,23,76,149,431,539,659,1343,2678,2939,6524,6929,8414,8873,
%T A282198 10027,25367,27299,87073,113071,122875,178595,185534,599237,1308195,
%U A282198 1888172,4803699
%N A282198 a(n) = k if the last Dyck path that is counted in A279286(n) is the k-th Dyck path.
%C A282198 Since there are 19 concurrent Dyck paths through diagonal position 19818 (not in A279286) that occur after 20 concurrent Dyck paths at position 18915 (in A279286), number 28594 does not occur in this sequence while 27299 does.
%C A282198 For more information about the Dyck paths mentioned see A237593.
%F A282198 a(n) = max( k : A279286(n) = A240542(k) ), for n >= 1.
%e A282198 a(4) = 23 since the point on the diagonal is A279286(4) = 15 and only A240542(20)..A240542(23) = 15.
%t A282198 a240542[n_] := Sum[(-1)^(k+1)*Ceiling[(n+1)/k - (k+1)/2], {k, 1, Floor[(Sqrt[8n+1]-1)/2]}]
%t A282198 a282198[b_] := Module[{centers={{1, 1}}, acc={1}, k=2, cPrev=1, cCur, len}, While[k<=b, cCur=a240542[k]; If[Last[acc]==cCur, AppendTo[acc, cCur], len=Length[acc]; If[First[Last[centers]]<len, AppendTo[centers, {len, k-1}]]; acc={cCur}; cPrev=cCur]; k++]; Last[Transpose[centers]]]
%t A282198 a282198[5000000] (* data *)
%Y A282198 Cf. A237593, A240542, A279286.
%K A282198 nonn,more
%O A282198 1,2
%A A282198 _Hartmut F. W. Hoft_, Feb 08 2017