[seqfan] Re: Sister sequences

[Neil Sloane]

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
>
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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.
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