Help with a Mathematician's Number?

Question

I was in a TA session for math a couple of weeks ago, and my TA was talking about some mathematician's set of numbers that could only be computed by computers in exponential (or was it logarythmic?) time. Because of this, only the first 4 have been found (even though an infinite number exist). Do any of you guys know what I'm talking about?

My TA gave the example of bringing friends to a party or something, but I didn't really follow. Anyone have any insight to what he/I am talking about?

Answer 1

Your description is quite intriguing!! Please ask your TA for more details. One possible fit is the Ackermann Function (and corresponding numbers). Busy Beaver numbers are another possibility. Fermat Primes might also be a possibility. None of those fit the "bringing friends to a party or something" example.

Please ask your TA and post again!

Answer 2

Current implementations of the 64bit architecture can address up to 1 tebibyte of RAM (2^40 bytes); the architecture permits extending this to 4 pebibytes (2^52 bytes) in the future
Going by this the 4 digits calculated thus far have to follow a function with a very high degree of exponentation to justify the large amount of calcuation time.
Very few functions follow this rule; although the example you mention might be a help.
I might like to belive as Phineas does that it is the Ackermann function or another recursive function for that matter but the example dosnt justify my theory.
Recursive functions are used for iterations and form a foundation of computation theory. For instance the Ackerman takes two positive natural numbers as arguments and gives the output in the form of a natural number.
The function is defined as the nth iteration of the mth loop for the two natural numbers n and m. As you can see the function takes a exponential form.
Please provide us with more data...

Answer 3

I think that you are talking about Ramsey Numbers and the Ramsey party problem:

What is the minimum number of guests at a party such that at least m will know each other or at least n won't?

The solution to this problem is called the Ramsey number R(m, n)

The value of R(5, 5) is known to lie between 43 and 49, but its exact value is unknown.

Answer 4

I couldn't find anything matching exactly these criteria.

There are only four known double Mersenne primes, but it is not known if any more exist. (See first two links below.)

Even more interesting, I found a category of numbers which has yet to be proved to contain any elements: Lychrel numbers (for base 10). (See third link below).

If you could remember any more information it would help.