[seqfan] Re: easy and bref

[Charles Greathouse]

That's a pretty hefty requirement; I don't think we should limit hard
to just such cases.

But I think I agree that it would be best to use it only when the
problem is known (in some sense) to be hard.  That doesn't mean it
couldn't be applied to a previously-undiscovered sequence, just that
it would need to relate to the current state of mathematical
knowledge.  (No one's studied primes of the form 25389789848938923^n +
2, but if there was something special enough about them the existing
knowledge about primes in exponential sequences should suffice to say
that it is hard in some sense.  Whether this is hard enough is
unresolved.)

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Sep 30, 2011 at 1:39 PM,  <franktaw at netscape.net> wrote:
> Thanks, that's an example of what Charles was looking for. The busy beaver
> problem is provably hard - we know that we won't be able to find a formula
> for it.
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: D. S. McNeil <dsm054 at gmail.com>
>
> ...
> I guess I don't see "hard" as a permanent property but as a
> description of our state of knowledge.  Right now, A060843 -- the busy
> beaver problem -- only has four known terms, and not for lack of
> interest.  Why only four?  Because the sequence is hard in the
> colloquial sense.  If someone comes up with a formula and we suddenly
> had lots of terms, we'd simply remove "hard", like we remove "obsc"
> after someone cleans up a sequence in bad shape.
>
>
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