[seqfan] Re: When is a sequence a list?

[Marc LeBrun]

I agree this sounds like it's probably being over-thought.  In practice it seems pretty simple:

In submitting a sequence, if there's a natural n0 that's the offset, then use that, and if not, then make the offset 1.  To elaborate:

If the sequence you are submitting is characterized by some definite mapping n-->a(n), and the sequence values you submit start from some n=n0, then you should specify the offset as n0.

Otherwise -- eg when index n only means a(n) is "the n-th" instance of something, and/or n0 doesn't matter, and/or you can't identify a unique natural n0 -- then the default is to make the offset 1.

As a simple example, consider A006933: 2, 4, 6, 30, 32, 34, 36,... the "eban numbers", whose English names do not contain the letter E.  There's no motivation to associate the initial value 2 with any specific index n0, so by convention to avoid confusion we always use the default offset of 1.

Surely that doesn't present much difficulty? 

This "default offset=1" situation is colloquially referred to as a "list" in the OEIS context -- however the "listness" of a sequence here isn't an intrinsic mathematical property of the ordered numerical values, but rather a concept that belongs more to the ontology of the OEIS metadata.