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 A226188 #10 Jan 04 2019 21:39:23
%S A226188 1,2,4,8,16,31,60,116,227,441,859,1674,3260,6349,12367,24088,46916,
%T A226188 91380,177984,346666,675214,1315136,2561536,4989191,9717617,18927334,
%U A226188 36865412
%N A226188 Least positive integer k such that 1 + 1/2 + ... + 1/k > 2n/3.
%C A226188 Conjecture: a(n+1)/a(n) converges to 1.94...
%C A226188 Conjecture confirmed: series expansion of HarmonicNumber(k) gives a(n+1)/a(n) -> exp(2/3) = 1.947734... [_Jean-François Alcover_, Jun 05 2013]
%e A226188 a(8) = 116 because 1 + 1/2 + ... + 1/115 < 16/3 < 1 + 1/2 + ... + 1/116.
%t A226188 z = 18; f[n_] := 1/n; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= 2n/3 &], {n, 1, z}]; m = Map[a, Range[z]]
%Y A226188 Cf. A226186, A226187.
%K A226188 nonn,more
%O A226188 1,2
%A A226188 _Clark Kimberling_, May 30 2013
%E A226188 More terms from _Jean-François Alcover_, Jun 05 2013
%E A226188 Deleted obsolete b-file. - _N. J. A. Sloane_, Jan 04 2019