A226895 Difference sequence for A226894.

3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2

Offset

1,1

Comments

The number of numbers log k between consecutive harmonic numbers is 1 or 2, so that the difference sequence for A226894 consists of 2's and 3's.

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Example

log 1 < log 2 < h(1) < log 3 < log 4 < h(2) < ..., so that the positions of h(1) and h(2) are 3 and 6, whence a(1) = 6 - 3 = 3.

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. A226894 , A226896 (complement).

Sequence in context: A321218 A259494 A356525 * A306996 A166007 A087497

Adjacent sequences: A226892 A226893 A226894 * A226896 A226897 A226898

Keyword

nonn,easy

Author

Clark Kimberling, Jun 21 2013

Status

approved