[seqfan] Re: Sister sequences
reinhard.zumkeller at gmail.com
Fri Nov 22 17:39:05 CET 2013
I added a b-file ...
showing a nice (if not remarkable) plot.
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
> or rather its negatives, as A232221. The plot doesn't look all that
> 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
> 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
> > _______________________________________________
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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.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
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