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

[Neil Sloane]

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
>
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