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

[Sean A. Irvine]

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.