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%I #11 Aug 18 2013 11:20:09
%S 3,6,9,12,14,17,20,23,25,28,31,34,37,39,42,45,48,50,53,56,59,62,64,67,
%T 70,73,75,78,81,84,87,89,92,95,98,101,103,106,109,112,114,117,120,123,
%U 126,128,131,134,137,139,142,145,148,151,153,156,159,162,164
%N Position of n-th harmonic number H(n) in the joint ranking of {H(k)} and {log k}, for k >= 1; complement of A226896.
%C If, in the definition, log k is replaced by g + log k, where g is the Euler-Mascheroni constant, then the position of H(n) is 2n, and limit[1/(H(n) - g - log n) - 2n] = 1/3.
%H Clark Kimberling, <a href="/A226894/b226894.txt">Table of n, a(n) for n = 1..1002</a>
%e log 1 < log 2 < H(1) < log 3 < log 4 < H(2) < ...
%t z = 300; h[n_] := N[HarmonicNumber[n], 100]; t1 = Table[h[n], {n, 1, z}]; t2 = Table[N[Log[n], 100], {n, 1, 3 z}]; t3 = Union[t1, t2]; p[n_] := Position[t3, h[n]]
%t Flatten[Table[p[n], {n, 1, 3 z}]] (* A226894 *)
%t Differences[%] (* A226895 *)
%t Complement[Range[z], %%] (* A226896 *)
%Y Cf. A001008(n)/A002805(n) (H(n)), A226895 (differences), A226896 (complement).
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jun 21 2013
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