I was wondering what the potential cardinality of the set of entries in the Online Encyclopedia of Integer Sequences (oeis.org) may be.
After all, if we consider the text box with its "Search" button, we're seeing a map from sequence IDs to sequence specifications. From this vantage the set of entries is not limited by physical storage. There could be a mathematical space of entries that are only materialized in storage upon request.
I've seen that the site has a policy to include interesting sequences, not uninteresting sequences. But I haven't seen a specification of what is "interesting" or "uninteresting". I'm not sure that the cardinality of the entry set is constrained by the "interestingness" criterion.
Now, are entries in OEIS required to be computable?
I mean, must there exist for each entry a finite-sized algorithm that would, given sufficient and perhaps infinite time, generate all of the sequence's elements? In that case we're limited to aleph-null entries, aren't we?
Do we know of any other constraints?
Is it OK if on math.se we discuss the specifics of OEIS in practice? I mean, if my question oversteps the bounds of propriety, please feel free to restrict answers to proper seriousness and relevance.
The size of the encyclopaedia at any time will be finite. This is determined by the finite storage capacity available (amongst other constraints).
Only countably many sequences will ever be described since we have a finite language with finite strings. If the universe is finite, storage capacity will always be finite.
There are uncountably many possible sequences. Therefore, for example, there are integer sequences which ultimately grow faster than any formula we can construct.