a(27) in A059097: A new lower higher bound

[Alonso Del Arte]

Accepting Naohiro Nomoto's statement as true that after 786 there are
no more terms less than 157430 in A059097, I've checked up to 160250
and found no more terms either. I've been checking in chunks of a
hundred each, my algorithm takes about 505 seconds for each chunk, 495
seconds if I don't do anything else on the computer.

Can anyone confirm or dispute my finding? Has anyone else tried to
extend this further? Anyone close to a proof that the sequence is
finite?

Alonso