[seqfan] Re: An equivalence for integer sequences (with more questions than answers)

N. J. A. Sloane njas at research.att.com
Fri Feb 27 00:12:57 CET 2009

Jaume made a very interesting comment, suggesting that we classify 
sequences { a(n): n >= 0 } by the value of Sum_{n >= 0} 1/a(n)

More generally, for a strictly positive sequence with offset O,
we can assign the value Sum_{n >= O} 1/a(n)

If the sum doesn't converge, assign the value "NA" (Not Applicable)

Even more generally, for a pair of sequences a(n), b(n),
we could assign the value of Sum_{n >= O} a(n)/b(n).

In fact the possibilities are endless for assigning numbers to
sequences or pairs of sequences.  Lim_{n >= O} a(n)/b(n), for example.


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