# [seqfan] Re: A079353

Neil Sloane njasloane at gmail.com
Thu May 29 20:56:33 CEST 2014

```I was hoping that someone would revise A079353 to take these comments into
account, but no one did it, so I've done it!

On Wed, May 21, 2014 at 4:34 PM, Robert G. Wilson v <rgwv at rgwv.com> wrote:

> et al,
>
>         I got really close with:
> fQ[n_] := Length@ Select[ Range[ Floor[ n/2], n], IntegerQ@ Round[
> HarmonicNumber@ n, 1/#] &] > 0; k = 3; lst = {1}; While[k < 10001, If[ fQ at k, Print[k]; AppendTo[ lst, k]]; k++]; lst
>
>         Also see https://oeis.org/A115515.
>
> Bob.
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of
> israel at math.ubc.ca
> Sent: Monday, May 19, 2014 9:10 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] A079353
>
> The data in this sequence don't seem to fit the definition:
>
>          Numbers n such that the best rational approximation to H(n) with
> denominator <=n is an integer, where H(n) denotes the n-th harmonic number
>
> The given data are
>
>         1, 3, 4, 10, 11, 30, 31, 82, 83, 226, 227, 615, 616, 1673, 1674
>
> For example, how does 10 fit in? H(10) = 7381/2520, and the best
> approximation with denominator <= 10 is 29/10, which is not an integer.
> Similarly, I don't see how 31, 82, 227, 616, or 1674 fit the definition,
> as according to my computations the best approximations in these cases are
> 125/31, 409/82, 1363/227, 4313/616, 13393/1674.
>
> Cheers,
> Robert
>
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--
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.