one-way versus two-way infinite sequences
Michael Somos
somos at grail.cba.csuohio.edu
Wed Dec 11 20:30:13 CET 2002
seqfan,
A question has recently come up about the implicit
assumption of one-way versus two-way infinite sequences
in the OEIS. My opinion is that all sequences in OEIS are
implicity one-way infinite unless specifically and clearly
indicated otherwise by some as yet unspecified mechanism.
There is good reasons for this.
Take for example, A000012. This is the all 1's
sequence. However, is the domain of this function all
integers or only non-negative integers? These are two
different functions. The non-negative integer version
matches the description of "continued fraction for golden
ratio". It matches "G.f.: 1/(1-x)" and "E.g.f.: e^x".
It matches "Multiplicative with a(p^e) = 1".
I am in no way deprecating the two-way infinite
version, but insist that it is a different object with
different properties. This is just the opening salvo of
a wider dialogue, but it all starts from the question :
"What is an integer sequence?" Until we face this question
and clearly and accurately answer it, we are fumbling for
answers and not on the same wavelength. Shalom, Michael
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