[seqfan] Re: Subtract if prime, else add

[Neil Sloane]

Lars,  Thank you for those two very interesting graphs for A309529!

This is the coin-tossing paradox (or arcsine law paradox) at work, I
think.  (Feller, Probability Theory and Applications, Vol. 1, Chap III):
the sequence will change signs infinitely often, but the gaps between times
when the sign changes get longer and longer.

I just created two similar sequences, A309216 and A309217, and again the
graphs have the same
"coin-tossing" appearance.


On Sat, Aug 10, 2019 at 5:59 AM Lars Blomberg <larsl.blomberg at comhem.se>
wrote:

> I have updated A309529 with graphs of 10^8 terms.
> /Lars
>
> -----Ursprungligt meddelande-----
> Från: SeqFan <seqfan-bounces at list.seqfan.eu> För Neil Sloane
> Skickat: den 7 augusti 2019 17:45
> Till: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Ämne: [seqfan] Re: Subtract if prime, else add
>
> Eric, A309529 and A309521 are an interesting pair of sequences!
>
> For A309529 (I did a bit of editing), it would be interesting to see what
> happens when we look at more terms - does the sequence stay positive, or
> does it go negative again at some point?
>
> Maybe Lars could look at it?  It would be interesting to see the graphs of
> the first X terms, for some large values of X !
>
> For the "primes" version, A309521 (again I did some editing), now that it
> has been approved, we need a b-file!  Lars's comments suggest that this one
> is going to keep growing for ever, unlike the first sequence.
>
>
> 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 Tue, Aug 6, 2019 at 6:24 AM Éric Angelini <eric.angelini at skynet.be>
> wrote:
>
> > Lars, be blessed among the blessed!
> > I will submit this asap to the OEIS!
> >
> > à+
> > É.
> > Catapulté de mon aPhone
> >
> >
> > > Le 6 août 2019 à 10:43, Lars Blomberg <larsl.blomberg at comhem.se> a
> > écrit :
> > >
> > >
> > > Up to 10^6 the terms increase approximately linearly, no cycles are
> > visible.
> > > The last terms are
> > > 3590238, 3590240, 3590242, 3590248, 3590251, 3590251, 3590257,
> > > 3590259,
> > 3590261, 3590267, 3590270, 3590279, 3590285, 3590287, 3590289,
> > 3590295, 3590298, 3590306, 3590312, 3590314, 3590316, 3590322,
> > 3590326, 3590326, 3590332, 3590334, 3590336, 3590342, 3590346
> > >
> > > Small values not encountered
> > > 2, 3, 6, 7, 13, 14, 19, 20, 24, 30, 31, 32, 33, 34, 35, 37, 39, 40,
> > > 41,
> > 42, 43, 44, 46, 49, 51, 53, 55, 56, 57, 58, 59, 60, 61, 66, 67, 68,
> > 69, 70, 75, 76, 77, 78, 79, 80, 81, 83, 85, 86, 87, 88, 89, 90, 91,
> > 92, 100, 108, 109, 110, 113, 114, 115, 116, 117, 118
> > > (same as for 1000 terms)
> > >
> > > /Lars
> > >
> > >
> > >
> > > --
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> >
> >
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