

A226894


Position of nth harmonic number H(n) in the joint ranking of {H(k)} and {log k}, for k >= 1; complement of A226896.


3



3, 6, 9, 12, 14, 17, 20, 23, 25, 28, 31, 34, 37, 39, 42, 45, 48, 50, 53, 56, 59, 62, 64, 67, 70, 73, 75, 78, 81, 84, 87, 89, 92, 95, 98, 101, 103, 106, 109, 112, 114, 117, 120, 123, 126, 128, 131, 134, 137, 139, 142, 145, 148, 151, 153, 156, 159, 162, 164
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OFFSET

1,1


COMMENTS

If, in the definition, log k is replaced by g + log k, where g is the EulerMascheroni constant, then the position of H(n) is 2n, and limit[1/(H(n)  g  log n)  2n] = 1/3.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1002


EXAMPLE

log 1 < log 2 < H(1) < log 3 < log 4 < H(2) < ...


MATHEMATICA

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]]
Flatten[Table[p[n], {n, 1, 3 z}]] (* A226894 *)
Differences[%] (* A226895 *)
Complement[Range[z], %%] (* A226896 *)


CROSSREFS

Cf. A001008(n)/A002805(n) (H(n)), A226895 (differences), A226896 (complement).
Sequence in context: A102014 A168045 A288522 * A091780 A331060 A329514
Adjacent sequences: A226891 A226892 A226893 * A226895 A226896 A226897


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jun 21 2013


STATUS

approved



