[seqfan] A new (or old), encompassing definition of Integer Sequences.
Antti Karttunen
antti.karttunen at gmail.com
Sun Feb 10 21:39:57 CET 2013
An integer sequence is a function Z -> Z (usually partial),
whose domain (*) is defined by an integer sequence.
(* in the first sense given in
http://en.wikipedia.org/wiki/Partial_function : "Most mathematicians,
including recursion theorists, use the term "domain of f" for the set
of all values x such that f(x) is defined.")
How about that?
Why so general? Then we can include also David Wilson's idea from
1999: http://list.seqfan.eu/pipermail/seqfan/2012-March/009214.html
Actually, now that I re-read it, it seems that his "index sequences"
is just the same as what I mean by the domain sequence here.
Note that the domains of the most infinite sequences in OEIS
have currently been defined with either A001477 or A000027.
(or with their characteristic functions on Z, if you so wish.)
Yours,
Antti Karttunen
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