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%I #18 Sep 10 2021 17:35:54
%S 4,11,22,36,54,75,100,129,161,197,236,278,325,375,428,485,546,610,677,
%T 749,823,902,984,1069,1158,1251,1347,1447,1550,1657,1767,1881,1999,
%U 2120,2245,2373,2505,2640,2779,2922,3068,3217,3370,3527,3687,3851,4019,4190
%N Least positive integer k such that 1 + 1/2 + ... + 1/n < 1/(n+1) + ... + 1/k.
%H Clark Kimberling, <a href="/A226183/b226183.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) = round(exp(gamma)*n*(n+1) + gamma) where gamma is the Euler-Mascheroni constant 0.57714... (A001620). - _Carl R. White_, Sep 01 2021
%F a(n) = A226184(n) + n. - _Michel Marcus_, Sep 09 2021
%e a(3) = 22 because 1/4 + 1/5 + ... + 1/21 < 1 + 1/2 + 1/3 < 1/4 + 1/5 + ... + 1/22.
%t z = 55; f[n_] := 1/n; p[n_] := p[n] = Sum[f[k], {k, 1, n}]; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= 2 p[n] &], {n, 1, z}]; m = Map[a, Range[z]] (* A226183 *)
%t m1 = Table[m[[n]] - n, {n, 1, z}] (* A226184 *)
%Y Cf. A226184, A289183.
%K nonn
%O 1,1
%A _Clark Kimberling_, May 30 2013
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