Players:

- NotAJumbleofNumbers, analyst
- StrangerCoug, algebraist
- Micc, analyst
- Jackal711
~~replaces Yimmy~~, algebraist

Replacements:

Previous winners:

- Implosion

How to join:

Type: "/in"

You may in after the game starts, I'll either add you to the replacements or just start you immediately -- the stealing mechanic should make it easy enough to catch up in points

Game flow:

- You start with 7 cards
- On your turn, play some cards in only one of these ways:
- Start one new sequence with at least 3 cards: "I'm playing 3, 9, 18 for divisible by 3." You are welcome to include a closed form if you can like { 3 | n } but you must translate this into English for the rest of the players.
- Continue one sequence you previously started: "I'm adding a 3 to my primes"
- Steal one sequence from somebody else: "I'm adding 4, and 16 to Plotinus' powers of 2"

- When the sequence has at least 7 cards in it, it is finished. You get n points, for finishing it, where n is the number of cards in the sequence, and the sequence is removed from the game.
- After your turn I replenish your hand up to 7 cards so you can be thinking about your next move while the other players go.
- If you cannot think of anything at all to do on your turn, you may pass
- If all players pass consecutively the game is over and whoever has the most points wins.
- If the deck runs out of cards I will ask if people want me to reshuffle it and keep going or start a new game. We can also discuss shuffling in a new deck.

Invalid sequences and exceptions:

- Most sequences are valid if you can tell us what the rule is. The rule does not have to be number theoretic; cosmetic rules are fine. They can be as complicated or as simple as you like, though for complicated ones it is worth checking the deck to make sure there are at least 7 such numbers. You don't need to collect the numbers of the sequence in order. There are just a few exceptions:
- A sequence is a set of numbers that all have something in common with each other. Numbers may not be excluded from sequences they would naturally belong to, for example "primes except 7".
- Variants of "all integers", "numbers less than 1001", "random numbers" -- these are all equivalent to "player 1 starts the game with 7 points for no reason"
- Repeats: if someone has already put 15 in the divisible by 5's sequence, you can't put another instance of 15 in it. This goes even for sequences that naturally contain repeats. fibonacci only gets one 1, or a naturally repeating sequence like [1, 2, 1, 2, 1, 2, 1, 2] would be disallowed.
- The variables used in closed forms must represent integers (ℤ). For example you may not say that 5 is a member of the sequence n
^{2}because the square root of 5 is not an integer. - Sequences that are the same or equivalent to a sequence that we already have, whether it is in active play or in the Finished category. For example if we already have the "divisible by two" sequence, we cannot also have the "even numbers" sequence. If we have "divisible by 3" then we cannot also have the "n = 0 mod 3" sequence. Once a sequence has been used it cannot be reused until we start a new game.

Bingos (putting down 7 cards at once):

- Your sequence should match less than or equal to half of the unique cards (55.5) in either the current deck or in the range [1,100], which may be less tedious to verify.
- If you are a following a meta rule to generate rules for sequences, then the meta rule shouldn't be able to generate sequences that are bingos for more than 1% of hands.
- An example meta rule that would generate a bingo all of the time is roots of the 7 degree polynomial (x - my first card)(x - my second card)(...)(x - my seventh card) = 0.
- Another meta rule for generating sequences "look up my hand in a large database of sequences" is also not allowed for bingos, so you should be able to show enough of your work that we can see you worked forwards not backwards.)

Activity Requirements:

- This post contains the order the players are in.
- If you see that it is your turn, you may go without waiting.
- If it has been your turn for 24 hours and you have not gone, I will prod you.
- If you don't go within 24 hours of being prodded we'll skip you.
- If you're skipped twice in a row I'll put you as inactive and autoskipped until you return. If someone is waiting to pay they will be given a new hand
- Let us know if you're going to be V/LA or want to go inactive.
- If you are inactive you must /re-in and be put at the end of the waiting list.
**Spoiler: deck**

Sample Game State:

Completed: { 3n - 1 }

K has:- [13, 28, 43] { f(n) = 15n + 13 } When you divide by 15, the remainder is 13
- [1, 2, 4, 16, 32, 64] { 2
^{n}} The numbers you get by repeatedly doubling 1

- [3, 9, 27] { 3
^{n}} The numbers you get by repeatedly tripling one. - [8, 10, 13, 18, 39] { f(0) = 7, f(n) = f(n - 1) + g(n); g(0) = 1, g(1) = 1, g(n) = g(n - 1) + g(n - 2) } Each number starting with 7 has the the next number of the fibonacci sequence added to it
- [5, 93, 343] { n is a preperiodic point of a fixed point in the map f(n) = n
^{2}in ℤ_{100}} When you repeatedly square these numbers and take the remainder after dividing by 100, these numbers converge on a single point which remains itself when squared, but they are not themselves that final fixed point. - [3, 21, 36, 51] { 3n } these numbers can all be divided evenly by three.

I am P and it is my turn. My secret hand is: [31, 21, 64, 21, 7, 3, 63]. I would like to complete K's powers of 2 and convert it into points but it already has a 64 so I cannot. I could put 63 into my 3n sequence but then it will only need 2 more before it gets completed. It is easy to steal because roughly a third of the cards in the deck can go into it, and the pattern is obvious. I think it is less risky to put the 7 into my sequence of periodic points. It fits the pattern: 7

^{2}= 49 mod 100, 49

^{2}= 1 mod 100, 1

^{2}= 1 mod 100, fixed point.

I write "adding 7 to the preperiodic points" or something that identifies it uniquely, the mod hands me a new card and the next person goes.