report on recent OEIS activity

[N. J. A. Sloane]

1.  Ralf Stephan has been going through the OEIS and 
comparing sequences via a table of first differences.
As a result of this data-mining he has uncovered many 
duplicate sequences, also a number of
pairs of sequences which appear identical although 
they have totally different definitions, also many
hitherto unknown formulae.

Thanks, Ralf!

I am merging the obvious duplicates, and I am recycling
the A-numbers.  So if you submitted sequences recently, even
pre-numbered ones, they may end up with small A-numbers.

For the conjectured duplicates, I am marking them by
saying something like:

%Y A059975 Is this the same as A087656? - Ralf Stephan, Feb 21, 2004

(that might also appear as a comment line)



2.  There has been some discussion recently on this mailing list
about sequences of this form:

"Numbers n such that the string n72n is prime"

I don't think these are interesting and I rejected them all.
There are too many of them, for one thing.

I also rejected sequences of the following type:

"Primes p which remain prime when the first digit is
replaced by 1, 2 or 7"

There are again infinitely many variations, all boring.



3.  In general sequences like the above which depend 
on the base-10 representation (i.e. having keyword "base")
are discouraged, unless they are really brilliant.

They are likely to be silently rejected, especially 
if you have a habit of sending in incorrect sequences.

Many of the duplicates sequences that Ralf has found
were because someone sent in an incorrect sequence,
which when corrected showed that it was in the database already.
I won't mention names, but there are about 4 people who
are responsible for this.

Another source of duplicates is this:  you submit a sequence,
and then later you find an error and you submit it again.
Or you find some more terms.
Or you were not sure the first submission was successful,
so you send it again.

If you do this, please put a comment saying "This is
a resubmission of a sequence that I sent an hour ago."

Otherwise the two versions may end up as two sequences,
if I don't happen to notice the duplication.


4.  Finally, I remind people that the standards of the OEIS are
those of a mathematics reference work.

Sequences must be absolutely correct.  If they are only guesses,
you are under an obligation to say so.

Say "The terms shown are the only ones that have been
proved to be correct. It is conjectured that the next
three terms are xxx, yyy and zzz."

It is an axiom that sequences in the OEIS do not change with time.
(Except to have more terms added.)

That's why, for example, the most recent Mersenne primes
are not yet included in A000043.  They are mentioned in 
extension (%E) lines, but not in the sequence itself,
because at prsent there is the possibility that smaller
Mersenne primes exist.



5.  Here is a new (?) sequence for which at present I only
know one term. 
"Numbers n such that the numerator of
Bernoulli B(2n) is divisible in a nontrivial way
by a square."
My example, found yesterday, is that
the numerator of B_284 is divisible by 37^2.
(37 is the first irregular prime, of course.)
So 142 is a member.

I am not saying that is the smallest example.  I am also
not saying what "nontrivial" means, for the correct meaning
of "nontrivial" should emarge from the calculation (2n should be
squarefree?  The square divisor should be relatively prime
to 2n??)


I will send this off before Cablevision crashes again.

NJAS