[seqfan] When is a sequence a list?

[Felix Fröhlich]

Dear SeqFans,

until recently, I thought I know pretty well which sequences are lists and
which are not. But now I am no longer so sure. Consider the following
example:

I think we all agree that A001220 is an example of a list. Now, suppose the
sequence b(n) = A001220(n)-1/A305184(n) were in the OEIS. It is clear
A001220 could be defined by the formula a(n) = A305184(n)*b(n) + 1.
Wouldn't that mean A001220 would no longer be a list?

This raises the question for me: Does the property of a sequence being a
list or not only depend on the definition used for the sequence? So being a
list is not a property intrinsic to a sequence? In particular, if A001220
is defined in the current way, it is a list, but if it is defined as a(n) =
A305184(n)*b(n) + 1, it is not? Even though the two definitions are
equivalent? That seems weird to me, because the two descriptions are of the
same sequence.

I hope someone can help clear this up for me.

Best regards

Felix