Sequences needing more terms: high-value targets?

[Maximilian Hasler]

> I apply the keyword "hard" to a sequence only if
> 1) I have expended at least an hour of computer time looking for the
> next term, and
> 2) I've thought about it carefully, and I find it very unlikely that
> there's another algorithm that could find it a lot faster than mine.

This is as I understand it also. However, sometimes one fails to
remark a simple pattern. E.g. for
http://www.research.att.com/~njas/sequences/A058429 :
I suspect that the next terms are
32645356640144805339103579127542660095683,
1065719310162246533488642668727242229836115845084364968718962458406456800068819599

Calculated in < 1 ms.... (Well, at least these are upper limits for
the next terms... I did not yet have time to think about the
possibility of smaller solutions.)
Also, I found the next term of A058429 in < 30 minutes on a slow
laptop with PARI (code submitted but does not yet appear on OEIS). I
noticed afterwards that it's already known, but I assume a much slower
algorithm had been used for the preceeding terms, else the next term
would have been put there at once.
All that just illustrates how it may be useful to put short sequences
on OEIS with kw more and maybe hard, even if later on someone else
recognizes (maybe) that ist's not "so" hard....

M.H.