[seqfan] Re: Duplicates
Joseph S. Myers
jsm at polyomino.org.uk
Sun Sep 13 18:42:04 CEST 2009
On Sun, 13 Sep 2009, Ignacio Larrosa Cañestro wrote:
> Sequences
>
> http://www.research.att.com/~njas/sequences/A001835
>
> (a(n) = 4a(n-1) - a(n-2); a(0) = a(1) = 1)
>
> and
>
> http://www.research.att.com/~njas/sequences/A079935
>
> are the same, except for a initial extrra 1.
There are actually lots of sets of sequences that are the same apart from
the initial terms, and have cross references from one to another to point
out this similarity (these two already have the cross references).
I don't think adding more such almost-duplicates is really encouraged -
you're meant to omit the initial terms when searching to see if a sequence
is already there, and can always add a comment to an existing sequence
about the significance of a variant with different initial terms - but at
the same time, having existing such variants present does help people who
search without omitting (enough) initial terms. And there are cases where
sequences agree except for initial terms but you don't really want to
consider them almost-duplicates (it would seem odd to consider all
sequences with only finitely many nonzero terms to be almost-duplicates of
A000004, for example).
See my previous comments about how it should be possible for OEIS to know
how such sets of sequences are related so that extending or adding a
b-file to one or extending a b-file has the effect of extending or adding
or extending a b-file for all the sequences in such a set. (This doesn't
need to be done by the core OEIS software; after the move to a wiki, an
externally maintained bot could propagate changes from one sequence to
another related sequence.) You could extend this idea by defining one
sequence in such a set to be the main sequence that gets all the comments
etc., and making the others just have the variant set of terms (so they
can be found by searches, used in transformations along with other
sequences, etc.) and a pointer to the main sequence.
Here are a few such almost-duplicate sets (from linear recurrences, like
the one you give) I've noticed before:
http://www.research.att.com/~njas/sequences/?q=id:A029744|id:A063759|id:A090989|id:A145751
http://www.research.att.com/~njas/sequences/?q=id:A016116|id:A060546|id:A131572
http://www.research.att.com/~njas/sequences/?q=id:A118658|id:A006355|id:A047992|id:A054886|id:A055389|id:A068922|id:A078642|id:A090991|id:A128588
http://www.research.att.com/~njas/sequences/?q=id:A003946|id:A025579|id:A027327|id:A052156
http://www.research.att.com/~njas/sequences/?q=id:A080923|id:A005051|id:A026097|id:A083583|id:A118264
http://www.research.att.com/~njas/sequences/?q=id:A025192|id:A008776|id:A027334|id:A099856|id:A110593
http://www.research.att.com/~njas/sequences/?q=id:A007052|id:A048580
I do not believe there are any *exact* duplicates (same initial terms and
offset) in these sets; they are just sequences whose only differences are
offsets and initial terms. There are already various cross-references
between the sequences in these sets pointing out the similarities. So I
don't think there's anything to change in OEIS at present regarding these
sequences, but it might hopefully be possible in future to create
better-defined links between such sets of sequences.
--
Joseph S. Myers
jsm at polyomino.org.uk
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