terms lack

[Lßbos ElemÚr]

On 6 Nov 06, at 22:45, Brendan McKay wrote:

> * Dean Hickerson <dean at math.ucdavis.edu> [061106 20:40]:
> > The terms that are listed in a sequence should be the start of the sequence.
> > If there are missing terms in between the listed ones, then the sequence
> > entry is not just incomplete, it's wrong.
> > 
> > If you've computed some terms of a sequence, but you're not sure if there
> > are smaller ones that you've missed, then you should only include the ones
> > that you're sure are at the start of the sequence.  You can add a comment
> > about the larger terms, stating that it's not known if there are smaller ones.
> > For example, the "EXTENSIONS" lines for the sequence A000043 (Mersenne
> > exponents) mention some recently discovered terms.  But there might be
> > some smaller ones, so these are not included in the sequence.
>  
> Is there an official rule about this?  I'm not sure it is correct.
> Of course we should not submit sequences with possible gaps, but
> suppose we can compute a(10) thru a(20) but have trouble with
> a(1) thru a(9).  I don't see why we can't submit a(10..20) with
> an OFFSET of 10 and a comment explaining why a(1..9) are absent.
> 
> Brendan.

There are 2 cases :
 1  -- You cannot even know how many terms are missing.
          This is essentally the case of eg Mersenne primes..
-------------------
 2. --  You can specify the missing terms by list-
          position. In this second case you can introduce 
          a marker signal to point to missing position.

Handling of the cases can follow different standard..
The general case can be worthwhile to publish if 
so many hard computation is behind. 
Ordering terms somehow it can be mentioned that
the sequence is lacunar.
With correct description the situation, the case is
neither wrong, nor good. Perhaps unnecessary...

The empty sequence represents the full lacunarity.
Quite correctly. However the empty sequence is
not unique. 

Labos