[seqfan] Re: F Numbers

franktaw at netscape.net franktaw at netscape.net
Fri Jan 9 00:52:09 CET 2009

This only addresses a fraction of the problems that I am trying to
address.  It deals with arrays indexed by non-dense sets of integers,
but not with sequences that do not consist of integers.  And
while you suggest ways to specify certain kinds of non-integer
indices, without a general way of specifying them, you are limited
in what non-integer indices can be used.

Specifying an index sequence for which a sequence is defined only
deals with maybe a third of the sequences of this sort.  For about a
third, the sequence is conjectured to never be undefined, which
would mean nothing actually changes; and for the final third, the
indices where the sequence is undefined are only conjectured.
(Note: these are off-hand estimates; I have made no effort to
actually count them.)

Franklin T. Adams-Watters

-----Original Message-----
From: David Wilson <dwilson at gambitcomm.com>

I really think the way this should be handled is to supply an index for
each sequence.


    join(x, y, z, ...) = { (x(n), y(n), z(n), ...) }


    tuple(x, k) = { (x(kn), x(kn+1), ..., x(kn+(k-1))) }


Sequences like "a(n) =
some function of n, or -1 if undefined" could be changed to "a(n) = 
function of n" with an index sequence containing only the values for
which a(n) is defined.


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