[seqfan] Re: like A004080 but for 1/(2i) and more

davidrabahy at comcast.net davidrabahy at comcast.net
Wed Jun 24 19:25:36 CEST 2020


Of course you are correct; I’m not sure how I got myself confused.  A014537 is the sequence I was looking for.

 

Is the diagonalization 1,3,4550,… interesting enough for an OEIS entry?

 

From: M. F. Hasler <seqfan at hasler.fr> 
Sent: Tuesday, June 23, 2020 11:48 PM
To: DavidRabahy at comcast.net
Cc: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: Re: [seqfan] like A004080 but for 1/(2i) and more

 

On Tue, Jun 23, 2020 at 10:33 PM David Rabahy <DavidRabahy at comcast.net <mailto:DavidRabahy at comcast.net> > wrote:

Least k such that H2(k) >= n, where H2(k) is the even harmonic number sum_{i=1..k} 1/(2i);
n
1 - 5
2 - 31
3 - 227
4 - 1674

 

Unless I'm wrong it should be 4, not 5, for n=1 above,

and more generally, A4080(2n), for obvious reasons :

 

Clearly this idea could be generalized, i.e. where Hq(k) is the qth harmonic number sum_{i=1..k} 1/(qi).

 

which is the same as H(k)/q, whence your sequence should be A4080(qn).

 

- Maximilian

 



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