A226894 Position of n-th harmonic number H(n) in the joint ranking of {H(k)} and {log k}, for k >= 1; complement of A226896.

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

Offset

1,1

Comments

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.

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: A337091 A168045 A288522 * A359213 A091780 A331060

Adjacent sequences: A226891 A226892 A226893 * A226895 A226896 A226897

Keyword

nonn,easy

Author

Clark Kimberling, Jun 21 2013

Status

approved