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Super weird to me that the OEIS only stores "first 180 or so characters of a number sequence". Of course that's going to completely mess up the analysis in the

Super weird to me that the OEIS only stores "first 180 or so characters of a number sequence". Of course that's going to completely mess up the analysis in the article. They do mention this. There's something strange to me about how often analysis doesn't have disclaimers like "0.1% of data wasn't available but we think that's fine" but more like "the writing samples were collected on napkins with Sharpie in a Denny's at 4am and every sample from someone with a last name starting the letters M-Z was lost in a fire" then goes on to make a bunch of conclusions about modern essay writing or something. Anyway, it'd be cool if the OEIS had the numbers up to some limit. Maybe 2^16 so it fits into two bytes. It would be at most 1.2MB per entry, but generally way way smaller.

yunruse 4y ago
As far as I'm aware, most OEIS sequences have a variety of different algorithms (Maple, Mathematica) to generate them. It would be nice to be able to extend these sequences out and see if this has any change to "Sloane's gap".
- ttctciyf 4y ago
  Try this one: https://oeis.org/A060843 https://oeis.org/A060843
  - travisjungroth 4y ago
    It's the Busy Beaver problem and BB-5 is proven ≥ 47176870. The list here would be the full list for any "up to n" database smaller than that.
    - ttctciyf 4y ago
      I'm just highlighting that some sequences are not so easily generated. BB(n) is canonically awkward in this regard.
adverbly 4y ago
> Super weird to me that the OEIS only stores "first 180 or so characters of a number sequence" I agree! Another opportunity for a paper though! If f(180) = y = 20067, what does the graph of f(x) look like? How quickly would f(x) grow? Linearly? Quadratic? Exponential? Logarithmic? Any bets?
- nneonneo 4y ago
  The problem is that f needs to be interesting. Nobody really cares about the function "17393/16200 x^2 - 14719/180 x", even if that produces f(180) = 20067.
  - adverbly 4y ago
    You misunderstood my point... f in this example is the function which computes the first number that does not show up in the first X samples of OEIS sequences(so in the paper cited, OEIS stores only the first 180, so when x is 180, f(x) = 20067). Interestingly, this will create a paradox because it could itself be expressed as an OEIS sequence, which would mean that it does not belong in the sequence... but if it doesn't belong, then it should belong(Russell's paradox anyone :D).
_ache_ 4y ago
Do you know that not every sequence is easily computable ? Like, most of them isn't. Even if you have an algorithm to compute them. I appreciate your optimism thought. But OEIS is made by pretty smart people, if it was so simple, it would have been made. It would be great to make it when possible but the bias will remains.
- saghm 4y ago
  I don't think they're criticizing the OEIS's approach for storing sequences, but the person who decided to use their prefixes to draw conclusions about which numbers are "boring".
- travisjungroth 4y ago
  > if it was so simple, it would have been made I don't believe this to be true. Maybe the people who make OEIS have been satisfied with having the description and a few examples. It would only work well for strictly increasing sequences. I don't know of any sequence that increases slowly and is difficult to compute. If it increases quickly, then you'll quickly pass the limit. If it's not increasing, then you'd have to prove which numbers are under the limit and that could be very challenging in some cases.
  - ratmice 4y ago
    The first thing that came to mind for slowly increasing worth looking into seemed like it might be the inverse ackermann function, which curiously I didn't find any OEIS entry for.
    - unkulunkulu 4y ago
      Inverse ackerman should be easy to compute by computing ackerman for enough terms and inversing numerically? I mean, it will be the same number basically for a looooong time
nneonneo 4y ago
It’s not actually true; the OEIS is capable of storing a lot more numbers per entry in the form of a “B-file”, for example: https://oeis.org/A000127/b000127.txt https://oeis.org/A000127/b000127.txt. You can see the documentation on this feature here: https://oeis.org/wiki/B-files https://oeis.org/wiki/B-files. As far as I understand it, though, these B-files aren’t indexed by the search engine.
- travisjungroth 4y ago
  Thanks! I looked around and didn't see that.

yunruse 4y ago

As far as I'm aware, most OEIS sequences have a variety of different algorithms (Maple, Mathematica) to generate them. It would be nice to be able to extend these sequences out and see if this has any change to "Sloane's gap".

ttctciyf 4y ago
Try this one: https://oeis.org/A060843 https://oeis.org/A060843
- travisjungroth 4y ago
  It's the Busy Beaver problem and BB-5 is proven ≥ 47176870. The list here would be the full list for any "up to n" database smaller than that.
  - ttctciyf 4y ago
    I'm just highlighting that some sequences are not so easily generated. BB(n) is canonically awkward in this regard.

adverbly 4y ago

> Super weird to me that the OEIS only stores "first 180 or so characters of a number sequence" I agree! Another opportunity for a paper though! If f(180) = y = 20067, what does the graph of f(x) look like? How quickly would f(x) grow? Linearly? Quadratic? Exponential? Logarithmic? Any bets?

nneonneo 4y ago
The problem is that f needs to be interesting. Nobody really cares about the function "17393/16200 x^2 - 14719/180 x", even if that produces f(180) = 20067.
- adverbly 4y ago
  You misunderstood my point... f in this example is the function which computes the first number that does not show up in the first X samples of OEIS sequences(so in the paper cited, OEIS stores only the first 180, so when x is 180, f(x) = 20067). Interestingly, this will create a paradox because it could itself be expressed as an OEIS sequence, which would mean that it does not belong in the sequence... but if it doesn't belong, then it should belong(Russell's paradox anyone :D).

_ache_ 4y ago

Do you know that not every sequence is easily computable ? Like, most of them isn't. Even if you have an algorithm to compute them. I appreciate your optimism thought. But OEIS is made by pretty smart people, if it was so simple, it would have been made. It would be great to make it when possible but the bias will remains.

saghm 4y ago
I don't think they're criticizing the OEIS's approach for storing sequences, but the person who decided to use their prefixes to draw conclusions about which numbers are "boring".
travisjungroth 4y ago
> if it was so simple, it would have been made I don't believe this to be true. Maybe the people who make OEIS have been satisfied with having the description and a few examples. It would only work well for strictly increasing sequences. I don't know of any sequence that increases slowly and is difficult to compute. If it increases quickly, then you'll quickly pass the limit. If it's not increasing, then you'd have to prove which numbers are under the limit and that could be very challenging in some cases.
- ratmice 4y ago
  The first thing that came to mind for slowly increasing worth looking into seemed like it might be the inverse ackermann function, which curiously I didn't find any OEIS entry for.
  - unkulunkulu 4y ago
    Inverse ackerman should be easy to compute by computing ackerman for enough terms and inversing numerically? I mean, it will be the same number basically for a looooong time

nneonneo 4y ago

It’s not actually true; the OEIS is capable of storing a lot more numbers per entry in the form of a “B-file”, for example: https://oeis.org/A000127/b000127.txt https://oeis.org/A000127/b000127.txt. You can see the documentation on this feature here: https://oeis.org/wiki/B-files https://oeis.org/wiki/B-files. As far as I understand it, though, these B-files aren’t indexed by the search engine.

travisjungroth 4y ago
Thanks! I looked around and didn't see that.