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%I #45 Jun 20 2017 23:43:17
%S 1,2,11,14,19,131,270,299,1906,6551,8448,110476,120698,274190,360430
%N Indices of records in A286720.
%C The records for the numbers of fractions are 4, 6, 8, 10, 12, 14, 16, 18, 22, 24, 26, 28, 30, 32, 34, ...
%t odd[n_]:=If[OddQ[n],n,n+1];a={};amax=0;n=1;While[Length[a]<25,lst={}; k=2n/(2n+1); s1=0; While[k>0,s2=odd[Ceiling[1/k]]; If[s2==s1,s2+=2]; AppendTo[lst, s2]; k=k-1/s2; s1=s2]; len=Length[lst];If[len>amax,amax=len;a=AppendTo[a,n]]; n++];a
%Y Cf. A228136, A286720.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, May 30 2017