[seqfan] Re: Sister sequences
Neil Sloane
njasloane at gmail.com
Fri Nov 22 17:50:55 CET 2013
The mountain peak at around n = 8000 is interesting! What happens next? It
would be nice to see a most extensive graph. We probably don't need a
bigger b-file (in A232221), but we could include a plot of the first 10^5
or 10^6 terms if someone would care to produce it.
Neil
On Fri, Nov 22, 2013 at 11:39 AM, Reinhard Zumkeller <
reinhard.zumkeller at gmail.com> wrote:
> I added a b-file ...
> showing a nice (if not remarkable) plot.
>
> Best regards
> Reinhard
>
>
> 2013/11/22 Neil Sloane <njasloane at gmail.com>
>
> > I can't really "see" a sequence until it is in the OEIS, so I added this
> > one,
> > or rather its negatives, as A232221. The plot doesn't look all that
> > remarkable,
> > at least for the first 47 terms. In this kind of "race", it is normal for
> > one sister to get ahead of the other and to stay ahead.
> > In the Index to the OEIS you will find
> > several entries related to "prime races",
> > see https://oeis.org/wiki/Index_to_OEIS:_Section_Pri
> >
> > Best regards
> > Neil
> >
> >
> > On Fri, Nov 22, 2013 at 3:23 AM, Veikko Pohjola <veikko at nordem.fi>
> wrote:
> >
> > > Dear seqfans,
> > >
> > > Consider the sister sequences a1=A077065 and a2=A077068, "Semiprimes of
> > > form prime -/+ 1". Let the corresponding sequences of the cumulative
> sums
> > > of the terms be s1 and s2, and let d be the sequence of the differences
> > > s1(n)-s2(n):
> > > d = 0, 0, 4, 20, 36, 52, 128, 216, 328, 464, 636, 796, 908, 1092, 1324,
> > > 1520, 1716, 1948, 2144, 2436, 2716, 2972, 3264, 3580, 3812, 4032, ...
> > >
> > > This nice and steadily growing (so it seems) sequence is not in OEIS.
> Its
> > > potential general interest is in its behavior, which is difficult to
> > > anticipate by intuition. Try it! The plot of d(n) is quite surprising.
> > >
> > > Veikko
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> >
> >
> > --
> > 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.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
--
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.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
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