[seqfan] Re: found a new sequence, not sure if interesting, and how to properly submit

[Neil Sloane]

That is interesting, but we already have a version of it:
https://oeis.org/A092318

Still, maybe it should be added to the OEIS - I'll do that.  But A092318 is
really the more fundamental version.

There are also the classic sequences A002387 and A004080

There's also an entry in the OEIS Index under "Harmonic"

Best regards
Neil

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.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sun, Jan 22, 2017 at 7:51 AM, Jerry V Polfer <polfer.jerry at gmail.com>
wrote:

> Since i'm new on this list, i'd first like to say hello to everyone.
>
> I'm not really mathematically trained (except the bits i learned in my
> mechanical engeneering studies), after leaving school and hating
> mathematics, i now found some newly developed interest in it, mainly by
> numberphile (and other) videos on YouTube.
>
> Inspired by such a video[1] called "Riemann's paradox: pi = infinity minus
> infinity" which was about Riemann series theorem,i had the idea for a
> sequence.
>
> According to this theorem, you can get that series to diverge to any number
> you want, by rearranging the terms. In the video it is done by first adding
> up as many positive terms as you need to get a sum >= n, then subtracting
> as many negative ones as you need to bring the total sum to a number < n,
> then continuing with positive terms and so on.
>
> So how many positive terms of the infinite series "1 - 1/2 + 1/3 - 1/4 +
> 1/5 - 1/6 + ..." do we need to add up to arrive at a sum >= n.
>
> n terms
>
> 1 1 (1=1)
> 2 8 (1+1/3+1/5+1/7+1/9+1/11+1/13+1/15=2.0218004...)
> 3 57 (sum=3.0032870...)
> 4 419 (sum=4.0006905...)
> 5 3092 (sum=5.0000417...)
> 6 22846 <22%20846> (sum=6.0000206...)
> 7 168804 (sum=7.0000017...)
> 8 1247298 (sum=8.00000009783...)
> 9 9216354 <92%2016%2035%204> (sum=9.00000004932...)
> 10 68100151 (sum=10.0000000072374...)
> 11 503195829 <50%2031%2095%20829> (sum=11.0000000001968...)
> 12 3718142208 <37%2018%2014%202208> (sum=12.0000000000281...)
>
> This numbers i did find using this script, a rather brute force method:
> http://pastebin.com/VaCXhfT6
>
> Interestingly, at least for me, the next number of terms can roughly be
> predicted:
> Number of terms for n = numbers of terms for n-1 * e^2
>
> Now i don't know if this sequence would be of any interest for the OEIS,
> and secondly how to properly submit, since i don't know any
> mathematica/maple code, and miss the knowledge of proper terms to describe
> it and formulate it in a formula.
>
> Can i submit it with nearly next to none extra information, and hope others
> clean up my mess, or should i refrain from submitting?
>
> Kind regards and sorry for the wall of text,
> Jerry Polfer
>
> [1] https://www.youtube.com/watch?v=-EtHF5ND3_s
>
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>