[seqfan] Re: A079353

Robert G. Wilson v rgwv at rgwv.com
Wed May 21 22:34:52 CEST 2014


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@ 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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