A106930 also primes x^2+63y^2

[Maximilian Hasler]

Let me give a "brainstorming" list of some points to consider:

(1) It would indeed be useful for OEIS users to see what statements
given in %C are conjectured and what statements are proved, unless the
given property is really obvious to "everybody".

(1b) I say "everybody" (which maybe should be clarified) since things
that are obvious or even trivial to some, may not be so to others (and
even, things one considers obvious on one day may seem completely
obscure on some later day, to the same person)

(2) It is clear that Neil cannot check all of the dozens of comments
he receives each day.

(3) Examples show that even experienced OEIS contributors may make
errors (not only typos...), so the signature of the comments is not
always sufficient as indicator to which degree it may be trusted.

(4) I agree it would look ugly to preface (almost) every comment (of
such type) by "Conjecture:", OTOH this might encourage people
"wandering by" and having some spare time, to write out the proof. I
think Neil has no objections of adding short to mid-sized a###.txt
files (or .html or .pdf) with proofs.

(5) Probably we have to accept that all comments (without explicit
proof) must tacitly be understood as conjectures.
(5a) A global disclaimer should state this for the whole of OEIS.
(Maybe already exists.)
(5b) What is worse, even the *definition* of a contributed sequence
may be in conflict to the submitted values (cf. (2)).
(5c) Added code makes it easier to cross-check quickly (insofar more
as it is written in a  language of a freely available CAS (like PARI)
or a common syntax understood by several different CAS (I think of
Maple which is almost compatible (say, very similar) to MuPAD and to a
large extend interpreted in "compatibility mode" by free software like
Xcas/GIAC and others)
and also, putting the code used to produce the sequence may more
easily allow to detect a possible error of reasoning made in
calculating the values.

(6) Maybe, on some day, there will be a version of OEIS with user
login and small clickable icons "I have cross-checked", "I have some
doubts", "I think here's an error", "I would appreciate a proof /
cross-check here", etc., which would allow for easy "half automated"
and asynchronous processing of such cases. (Further options: RSS /
e-mail notification of updates,....)

As a concluding remark, I also plead guilty of saying "I know how to
prove, but I don't have the time to write it down..." (I know I still
have some "debts" of this kind in my TO-DO list...)
This is of course very bad behaviour.. :( !

Maximilian

On Thu, Apr 24, 2008 at 4:35 AM, Artur <grafix at csl.pl> wrote:
> A106930 <http://www.research.att.com/%7Enjas/sequences/A106930>
>  Primes of the form primes x^2+63y^2