

A226895


Difference sequence for A226894.


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, 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
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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



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 *)
Complement[Range[z], %%] (* A226896 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



