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

[Hugo Pfoertner]

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.
>
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> Seqfan Mailing list - http://list.seqfan.eu/
>