The answer is 2428912878^5+2428912878, which we shall call A.
The next value after that is then A^6+A.
The key to analyzing it was noticing that it recursively recalls the last value along with an exponent (although there is a debatable formulaic issue of going from 0 to 1 since 0^0 is undefined).

Do I have the right answer, Riot?

Yes, that's basically correct. 0^0 = 1, though. It isn't undefined.
So the first part of the sequence was 0 + 0^0 = 1, then 1 + 1^1 = 2, 2 + 2^2 = 6, 6 + 6^3 = 222, etc etc.

Ehhhh, 0^0=1 is only true by convention or consensus because it requires limits. As it stands, 0^0 is undefined, but it is not worth fighting over, I think.

Here is my puzzle. This is a finite puzzle, so it does not go on forever, and as a hint, it involves two types of "transformation" and there are exactly three values remaining.

1C, 3, 1, 13, 16, 14, 22, 13, 4

9, -3, -10?

It's been so long since I've done transformations but the recurring 13 and the fact there's another 3 numbers makes me suspect a translation and a rotation?. The Translation being 3 + 13 = 16, and 1 + 13 = 14. 3 + 1 + 4 + 14 = 22, too. So every number there can be made from the rest, excluding the 1C.

1C is 28 in hex, which can be made from the other numbers there.

Nope.

Oh, so it is. Thanks, jmo.

1C, 3, 1, 13, 16, 14, 22, 13, 4

Bump for people to solve. :)

6, 13, 7?

Nope. And it's almost 24 hours.

I'll be generous and make this a 48-hr puzzle for people can have time. I don't want ghug or uclabb to say that they didn't see it.

Com'on folks. :)

Waiting to be solved:

1C, 3, 1, 13, 16, 14, 22, 13, 4

I'm late to this party, so I'm not sure of the rules. If questions are allowed: Zultar, can your sequence also be written as: 28 3 1 19 22 20 34 19 4? (Is your sequence written in base 16?)

Hey A_Tin_Can,
Basically there is a sequence of numbers/values (anything in ASCII) based on some rules such as the squares of prime numbers or if odd, do this and if even, do this and your job is to figure out what the rule is (or rules are).
So in the previous puzzle, Riot gave us 0, 1, 2, 6, 222, and 2428912878, which I figured out was the last number in the sequence raised to an ascending integer exponent plus that last number (i.e., 6=2^2+2, 222=6^3+6, 2428912878=222^4+222). This is an infinite sequence as we can always make more numbers.

So, the challenge is to figure out what would be the last three values in my finite puzzle, which as a hint involves a two step process:

1C, 3, 1, 13, 16, 14, 22, 13, 4

You can of course choose to write those values as anything you wish, but it may or may not help you. :)
In other words, I am not answering your question.

Well 1C does indicate some hexadecimal numbers, the question would be, are all the numbers hexadecimal ? could be that from one number to the other, one of the transformation is from decimal to hexadecimal...

It could also be base-13, Braillard. It's hard to know when there's only a C.

Ha, right semck.... then maybe Zultar, you could give us a hint there? Are all the number in the same base?

I agree with zultar that he shouldn't have to answer that, even not knowing the answer myself. Play around with all the possibilities, that's the point.

Since there are only going to be 12, I was wondering if it might be something to do with the months. But I didn't come up with anything.

Part of the fun of figuring it out, eh? :)

I thought to translate them into letters but got nothing

In base 13, they'd be: 25, 3, 1, 16, 19, 17, 28, 16, 4

In Hexadecimal: 28, 3, 1, 19, 22, 20, 34, 19, 4

I am going to look for any patterns in the binary later, but figured I'd post now in case anyone wanted to look first.

1C, 3, 1, 13, 16, 14, 22, 13, 4

0001 1100, 0011, 0001, 0001 0011, 0001 0110, 0001 0100, 0010 0010, 0001 0011, 0100

Nothing appears except 0's and 1's!

Ok, due to multiple people asking, I will give one last possible hint without giving the puzzle away: the puzzle is definitely related to webdiplomacy.

Well the static things on the site are limited. They include user id's, stats of banned people, join dates, and gameid's.

Transformations involving something from WebDip? Good god.

Well, I figured the first puzzle I give out should be an easy one so people would bite. I couldn't do a hard puzzle the first time. :)

Something about neutral supply centers perhaps?

Well, assuming the numbers are all in Hex, these are the territories pointed to by those IDs (on the classic map):

Ukraine, Liverpool, Clyde, Serbia, Constantinople, Bulgaria, Sweden, Serbia, Yorkshire.

Regardless of the base, I don't think it's the supply centres unless some other translation needs to be done - since there are repeated numbers in the sequence.

If anyone wants them, the IDs for the neutral supply centres (of which there are 12) are:

7 (Portugal), 8 (Spain), 17 (Greece),19 (Serbia), 20 (Bulgaria), 21 (Rumania), 33 (Finland), 34 (Sweden), 35 (Norway), 36 (Denmark), 43 (Holland), 44 (Belgium)

If we're getting technical, there is also 76+77 (Spain nc/sc) and 80/81 (Bulgaria nc/sc).