Is there a feasible way to passively crosscheck sequences against the OEIS database?

Question

What this questions is not: Can I access OEIS from Mathematica?

This topic has been raised more than once and has been well addressed.

Here's the situation as it seems to me:

• OEIS is a tremendously useful resource for certain branches of mathematical research. That it would pair well with Mathematica is obvious, and can be seen when WolframAlpha picks up on a sequence for you.

• What I really want is to figure out a low-impact way to monitor my active notebooks in near to real-time for any matches or partial matches to the sequence database, then adding a callout cell or something letting me know that "this sequence is A2345, click here for more" and all. Note that I refer here specifically to a passive monitor for known sequences, in the sense of being carried out constantly, but automatically and transparently.

• Here's what's tripping me up. I suspect that with the tools available, I could cobble together something pretty close to what I just described in the previous paragraph. However, in order of least to most, these are what I see as relevant issues:

  1. The overhead of constantly checking my notebooks and then running partial sequences past OEIS definitely sounds like it could have some obnoxious performance drag, unless implemented tightly.
  2. This also strikes me as breaking the golden rule; if everyone had this running, it could seriously interfere with OEIS for all I know.
  3. The "right" solution to me seemed to be to download a local mirror of OEIS (at least a partial copy of the more popular sequences), and use that for everything. The speed of your checks would be vastly improved, and you wouldn't be stepping on anyone else's internet. Unfortunately, I believe the last couple times I looked, the OEIS has some no-mirrors policy, and I can never remember why that is (unless protecting valuable work-product, which I get). I would think something like OEIS should be spread around, lest it be lost all at once after a couple of unfortunate and unforeseeable coincidences pile up.
  4. To some extent, I would expect this to benefit OEIS, both in further elaboration on the number of values recorded and properties of its sequences, as well as a higher sequence ingestion rate. I'm sure it's easier to be working on an interesting sequence in Mathematica and notice, "hey, this must not be on OEIS"; it's obviously unrealistic to be very diligent about it otherwise.
  5. This seems like a really useful feature to have in Mathematica, particularly for certain types of researchers. I would expect that many, many hours would be collectively saved by people immediately being able to see, "Okay, that apparently gives me an inverse-Pythagorean-primes progression, now why would that be..." (or if not that, insert some equivalent which is sufficiently obscure, befitting your level of math prowess.)
  6. I would even expect, if this saw moderately wide use, to help along some breakthroughs which may have otherwise been missed. Maybe after some data that popped up and looked unremarkable triggered a notification which led you down an alley you otherwise wouldn't have considered, etc.

As I said, I'm aware that much of this functionality already exists in one way or another, although to my knowledge, it almost always requires you actively making an effort to check. What I really want to know is:

1. Does this sort of integration sound appealing to others?
2. Can anyone think of a reasonable way to implement something that approximates the passive approach I advocated here without undue stress on any systems? Or, am I way overestimating the impact that would cause?