[seqfan] Re: Reproducing A064690 (sign changes of a rational fraction iteration)

[Sean A. Irvine]

Thanks Hugo and Lucas.

My exact computation matches your results to 1506, but there is little hope
that my computation will reach your next block of results.

I am still somewhat concerned that the precision needed might be very high
to be certain the numbers starting at 1081319 are correct, but perhaps the
plots you have produced will be sufficiently convincing that there are no
intervening terms?

Either way it is clear the latter terms in the published sequence are
incorrect. For the moment I have modified (in draft) the terms as far as
1506 but if you are confident then feel free to add further terms.

Sean.


On Sun, 23 Jul 2023 at 17:15, Hugo Pfoertner <yae9911 at gmail.com> wrote:

> Using PARI with floating point arithmetic, the results are stable for \p
> 100, \p 1000, \p 10000
> 2, 4, 7, 11, 13, 22, 23, 332, 560, 565, 566, 568, 616, 618, 1161, 1163,
> 1167, 1194, 1298, 1317, 1321, 1329, 1360, 1370, 1371, 1373, 1374, 1376,
> 1386, 1391, 1503, 1506, (confirmed with \p 100000)
> then no further terms until 10^6.
> After 10^6, using \p 5000 and \p 10000, I get up to 2*10^6:
>  1081319, 1081322, 1081349, 1081353, 1081356, 1081358, 1081363, 1081365,
> 1081367, 1081376, 1081379, 1081381, 1081385, 1081403, 1081414, 1081416,
> 1108352, 1108383, 1108384, 1109306, 1109307, 1109396, 1109499, 1109501,
> 1109508, 1109510, 1109511, 1109985, 1109987, 1109989, -111, 1110056,
> 1110058, 1110066, 1110068, 1110111, 1112866, 1112873, 1112875, 1112879,
> 1112972, 1112983, 1112989, 1113010, 1113020, 1113026, 1113028, 1113472,
> 1113474, 1113521, 1113523, 1113534, 1113536, 1113577, 1113584, 1113646,
> 1113648, 1113650, 1113655, 1126587, 1126589, 1126590, 1126594, 1126598,
> 1126629, 1126630, 1126638, 1126640, 1126643, 1126651, 1126664, 1126673,
> 1126682, 1126684, 1126686, 1126687, 1126690, 1126692, 1126694, 1126695,
> 1126712, 1126713, 1126715, 1126806, 1126808, 1126891, 1126893, 1127063,
> 1127065, 1127066, 1127069, 1127079, 1127098, 1127102, no further terms up
> to 2*10^6.
>
> Hugo Pfoertner
>
> On Sun, Jul 23, 2023 at 5:26 AM Sean A. Irvine <sairvin at gmail.com> wrote:
>
> > I'm finding reproducing A064690 surprisingly difficult despite its simple
> > definition:
> >
> > https://oeis.org/A064690
> >
> > It is my suspicion that the later terms were computed with insufficient
> > precision.
> >
> > Computing it exactly using rational arithmetic seems too slow to reach
> the
> > values listed.  Instead, I computed (using constructible real arithmetic
> --
> > which in theory should also be correct): 2, 4, 7, 11, 13, 22, 23, 332,
> 560,
> > 565, 566, 568, 616, 618, 1161, 1163, 1167 but this does not match
> existing
> > terms beyond 568.
> >
> > Could someone please make an attempt to verify (or come up with a better
> > way to compute this sequence) ?
> >
> > Sean.
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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>