[seqfan] Re: Some questions about the %O directive

Charles Greathouse charles.greathouse at case.edu
Thu Sep 24 22:52:47 CEST 2015


I have no preference here, but I count ~450 sequences with only one offset
number in the OEIS now. Should all have ",1" appended?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Thu, Sep 24, 2015 at 4:36 PM, Neil Sloane <njasloane at gmail.com> wrote:

> I prefer the rule as stated in the old help files: the default value
> for the second offset should be 1 (rather than omitting it altogether)
>
> Omitting it makes it look like an error. I set things up with this
> convention 30 or 40 years ago, so naturally I prefer it!
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Thu, Sep 24, 2015 at 2:57 AM, Sidney Cadot <sidney at jigsaw.nl> wrote:
>
> > Hi all,
> >
> > I'm in the process of fixing a bunch of minor issues that can be
> > detected programatically.
> >
> > I am now starting to check if I can find/fix issues with the %O
> directive.
> >
> > For some entries, the "%O" is missing altogether. As far as I
> > understand this should happen if-and-only-if the sequence has the
> > keyword 'allocated'; is that correct?
> >
> > For other entries, the %O line looks like one of these:
> >
> > %O a,b                (mostly) - or -
> > %O a                   (only sometimes)
> >
> > In both cases, the 'a' entry denotes the smallest integer index for
> > which the sequence is defined, i.e., a(p) is defined only if p >= a.
> >
> > The second number (if present) indicates the _position_ of the first
> > sequence value whose absolute magnitude exceeds 1. This always counts
> > from 1 for the first element in the sequence. So if 'q' denotes the
> > smallest valid index for which |a(q)|>1, b = q - a + 1. Is this
> > interpretation correct?
> >
> >
> >
> > Now as to the presence of the 'b': Charles Greathouse wrote last week:
> >
> >     "Sequences for which all terms are in {-1, 0, 1} should have only the
> > first
> > offset number."
> >
> > However, this is contradictory to the rule found in
> > http://oeis.org/eishelp2.html:
> >
> >     "In the internal format, there is a second offset, which says
> > which term (counting from the left, and starting with 1), first
> > exceeds 1 in absolute value. This is set to 1 if all the terms are 0
> > or +-1. "
> >
> > This latter rule is reinforced by the explanation given in
> > http://oeis.org/eishelp1.html:
> >
> >     "On the other hand, in this sequence (A010051) no term exceeds 1,
> > so b takes its default value of 1."
> >
> > Which rule is the correct one? (I personally feel that the rule given
> > by Charles is the cleaner one.)
> >
> >
> >
> > Lastly, there are a few questions on corner cases:
> >
> > - What do we do if |a(q)| > 1 only for a known large number of q
> > (beyond the values recorded in the OEIS?)
> > - What do we do if it is known that |a(q)| > 1 for some value of q,
> > but the value is not known (or not representable using normal number
> > notation, e.g. q = 10^(10^100))?
> > - What do we do if it is unknown whether |a(q)|>1 for any q?
> >
> > For most sequences, such issues will not occur, but I am curious how
> > close we can get to a mathematically precise definition of the
> > intended meaning.
> >
> > Regards Sidney
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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>
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>


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