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

Neil Sloane njasloane at gmail.com
Thu Sep 24 22:36:45 CEST 2015

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 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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