Composites, emirps, and emirpimes among de Polignac numbers (A006285)

[Jonathan Post]

Roland Bacher and Andrew Weimholt make good points.

As to "'emirps' sequence hardly deserves mention in the first place"
-- is the issue the name (emirp = prime spelled backwards, because by
definition an Emirp is a prime whose reversal, base 10, is a different
prime)? Similarly, Emirpimes: numbers n such that n and its reversal
are distinct semiprimes.

That is, what repels people: the use of a base sequence, the name, or
the lack of conjectures?

As to conjectures, for A006285 Odd numbers not of form p + 2^x (de
Polignac numbers), I'd mentioned "Law of small numbers can fool one
into thinking them all noncomposite, as the first 13 are." My guess is
that the typical readers, spot checking the first few of the dozen
initial values of A006285 might fall into the trap of assuming them
all to be primes.  My surprise, after formulating and disproving that
conjecture, was to find out that many of the initial primes were a
special kind of primes, and the same with the composites.

Hence my wondering what the statistics are if one looks further.
There are b-lists for these sequences. What are the densities of
primes in de Polignac numbers?  Of emirps in primes?  And so forth.

The reason I'd emailed seqfans is that these preliminary results and
questions are not so interesting as to make it clear that there's
anything submittable, except perhaps a comment to A006285 that,
coincidentally, the first 13 values are noncomposite, but that
composites abound thereafter.

In deference to njas, I prefer NOT to submit a sequence unless I have
good reason to believe that someone will find it interesting or
useful.

That reticence is part of what I feel distinguishes me from some
others of "the usual suspects." Also, per my previous email which njas
said he liked, on guidelines for new submitters, that 148 of my seqs
so far hotlink to arXiv papers in Math, Physics, or Biology, with a
couple more in the pipeline.

To be a mathematician, with rare exception, means that one must READ
the Math papers out there, and have at least some ambition to write
and conventionally publish them. To read, as I've said, is to read
ACTIVELY, with pencil in hand, or calculator window open on the
browser, playing the the assumptions and boundaries of the sequence's
formulae and definition; and looking at other seqs cited (and the
papers or websites linked to).

The ways in which OEIS is a modern form of publication are very
interesting, and the co-evolution of OEIS and seqfans is a major test
of ideas about the future of Math and of publication.

Thank you very much for your active, honest, and kind responses,

-- Jonathan Vos Post

On 6/19/08, Andrew Weimholt <andrew at weimholt.com> wrote:
> On 6/18/08, Jonathan Post <jvospost3 at gmail.com> wrote:
>  >
>  > Again, I know that njas and many others dislike "base" sequences.
>  > But, to me, the intersection of two OEIS seqs is (if not too sparse) a
>  > legitimate submission.
>  >
>  > Anyone have an opinion on this? Or an extension?
>  >
>
>
> IMHO, for an intersection of two sequences to be worthy of being in
>  the OEIS requires...
>
>  (1) that the both sequences themselves be interesting and noteworthy
>  (2) that there be some evidence of a mathematical relationship between
>  the two sequences (other than that the intersection is not too
>  sparse).
>
>  Your proposed sequence meets neither of these, as the "emirps"
>  sequence hardly deserves mention in the first place, and so far there
>  is no grounds to make a meaningful conjecture about why the two
>  sequences should even be mentioned in the same breath.
>
>
>  Andrew
>