Sequencer | StrangerCoug's turn

[Yimmy]

94, 41, 15, 12 to finish DeathRowKitty's "slots never touched by Ace, 5, or 9 in perfect out-shuffles of standard 52 card decks, mod 52"

[StrangerCoug]

I propose adding 1, 3, 9, 27, 81, 243, 729 to StrangerCoug's deck, or at the very least adding 243 in, because it is sad that you can only put 6 numbers in 3^n.

Sure Let's add them all.

[DeathRowKitty]

Whoa, someone actually used the out-shuffles sequence. I thought everyone had just decided to ignore it forever.

For the record, allowable congruence classes were:
6, 11, 21, 41, 30, 8, 15, 29
12, 23, 45, 38, 24, 47, 42, 32
and 52

grouped and ordered above based on cycles of individual cards during the shuffles.

[Plotinus]

Spoiler: Finished sequences:

• [5, 9, 10, 27, 48, 66, 98] {
  n² ± [0, 2]
  } numbers within 2 of a perfect square,
  
• [13, 15, 51, 53, 55, 73, 91] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i ≡ 1 (mod 2) ∀ i ∈ [1, 9], ∀ d > 0
  } numbers with at least two digits, all of which are odd
  
• [10, 21, 23, 45, 46, 59, 70] {
  n is 0 or odd (mod 9)
  } numbers that are odd when you repeatedly sum their digits
  
• [6, 7, 8, 13, 18, 20, 24, 34, 40] n is the sum of the Scrabble point values of the letters in the US spelling of the numbers in the deck.
  
• [12, 20, 35, 62, 85, 95, 100] numbers that are the sum of the proper divisors of some number < 1000 not in the deck for this game.
  
• [11, 17, 19, 29, 43, 71, 83] primes
  
• [5, 6, 13, 15, 16, 27, 100] numbers used in 0, including substrings of other numbers, but not including the deck spoiler
  
• [10, 21, 56, 57, 64, 76, 729] integers n for which there exists some integer m such that (n-1)/3^m and (n-2)/3^m are each endpoints of intervals removed during (possibly different) steps of the usual construction of the Cantor set (i.e. the construction in which each step removes the middle third of intervals existing after the previous step)
  
• [1, 10, 15, 28, 36, 78, 120] {
  n*(n-1)/2)
  }: triangular numbers
  
• [1, 4, 9, 16, 25, 64, 81] {
  n²
  } squares
  
• [7, 8, 9, 25, 37, 47, 49] {
  p^k | p^k < 50, prime p, k > 0
  }
  \
  {
  19, 27
  } numbers less than 50 with exactly 1 prime factor
  
• [12, 15, 19, 34, 35, 45, 49] 2 digit numbers with increasing digits
  
• [7, 14, 35, 42, 56, 63, 343] {
  7n
  } divisible by 7
  
• [8, 18, 29, 79, 87, 92, 96] {
  maxdigit(n) > 7
  } numbers that contain an 8 or 9
  
• [3, 4, 5, 7, 21, 22, 64] the nth prime doesn't have any even digits
  
• [1, 3, 6, 26, 54, 80, 220] numbers n for which there exists some positive integer with exactly 2n primitive roots
  
• [4, 13, 18, 27, 72, 88, 97] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k^2 | a_i ≥ 0, d > 0, k ∈ ℤ
  } numbers whose digit sum is a square
  
• [3, 21, 24, 33, 39, 84, 165] {
  3n
  } multiples of 3
  
• [1, 2, 4, 16, 32, 64, 256] {
  2ⁿ
  } powers of two
  
• [2, 3, 8, 23, 32, 56, 89] Numbers where each pair of consecutive digits differ by exactly one
  
• [1, 3, 5, 35, 74, 90, 512] numbers n for which there exists no way to make change for a dollar using exactly n coins, each of which may be a penny, nickel, dime, or quarter, without using at least one penny, one nickel, and one dime
  
• [10, 28, 36, 45, 50, 86, 93] numbers with exactly 2 distinct prime factors
  
• [1, 2, 8, 11, 20, 512, 1000] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 2^k | a_i ≥ 0, d > 0, k ∈ ℤ
  } sum of the digits is a power of 2
  
• [1, 2, 8, 11, 21, 89, 99]Numbers where any consecutive digits differ by at most 1
  
• [12, 15, 38, 41, 82, 84, 94] slots never touched by Ace, 5, or 9 in perfect out-shuffles of standard 52 card decks, mod 52

Implosion has 56 points and:

• [30, 42, 65] Composite squarefree numbers where when you take the sum of prime factors and write it in english, at least 1/3 of the letters in the word are "e"
  
• [9, 17, 69, 77] {
  n ≡ 1 (mod 4) ∧ n ≥ 7 (mod 10)
  } Numbers congruent to 1 mod 4 whose last digit, written in english, can have the letters "ty" appended to the end of it to multiply it by ten (e.g., "six" times ten is "sixty", but "fourty" is not a number, so the last digit cannot be four)
  
• [5, 6, 50, 125] Numbers such that if you take the number of letters in the english spelling and add that to the number, and then repeat that process a second time, the result is in the range 11-15 mod 50 (inclusive).

DeathRowKitty has 51 points and:

• [1, 31, 61] numbers relatively prime to 210

Yimmy has 21 points:

• [55, 58, 60] {
  n, k, c st n is composite; k - c is perfect; c|n; k = max(d) st d|n ∧d ≠ n
  } composite number whose greatest non-trivial divisor minus any of its other divisors is a perfect number
  
• [30, 40, 55, 75] {
  25 + (5n * (n + 1) / 2)
  } 25 + 5n, where n is a triangular number
  
• [2, 14, 17] numbers that are prime when their digits are reversed

StrangerCoug has 28 points and:

• [5, 7, 10, 14] {
  n*(n-1)/2) + 4
  } triangular numbers + 4
  
• [4, 20, 36, 52, 68] {
  16n + 4
  } remainder is 4 when dividing by 16

There are 0 cards left in the deck. It is StrangerCoug's turn. The game will continue until all 4 people pass in a row.

[StrangerCoug]

Pass

[NotAJumbleOfNumbers]

WAIT this game isn't Sequence?

i wonder if i could /in now...

[Plotinus]

WAIT this game isn't Sequence?

i wonder if i could /in now...

we're starting a new round soon with a new deck and slightly different rules, and we'd be glad to have you. It is probably not Sequence because it is a game I made up.

It is implosion's turn

[implosion]

pass.

[Plotinus]

It is DeathRowKitty's Turn

[StrangerCoug]

WAIT this game isn't Sequence?

i wonder if i could /in now...

we're starting a new round soon with a new deck and slightly different rules, and we'd be glad to have you. It is probably not Sequence because it is a game I made up.

Sequence is essentially a commercial version of One-Eyed Jack, though it's not clear to me which came first.

[Plotinus]

we can brainstorm a more interesting name for it perhaps.

[StrangerCoug]

I don't think it's that critical unless you're trying to release it commercially, but something that invokes rummy? Seqrummy, perhaps?

[DeathRowKitty]

pass

[Plotinus]

It's Yimmy's turn.

[Yimmy]

pass

[StrangerCoug]

And I think that makes game over with implosion the winner.

[Plotinus]

congrats, implosion!

In round 2 we will play with StrangerCoug's deck and we'll play in teams of 2 players. What other changes do we want to make to the prototype for this round?

[implosion]

gg.

[StrangerCoug]

Good game.

/in

[Yimmy]

do i have to /in again?
/in

[NotAJumbleOfNumbers]

Popping in here to say that yes, I do want to play.

[implosion]

I'll sit out the next game; may play more in a future game though if it's still going.

[Plotinus]

That's three players so far, I think we'll start when we have four.

[Plotinus]

I've PMed DeathRowKitty to ask if she's interested in round two, but I haven't heard back yet.

I'm going to be away next Thursday-Saturday but hopefully it won't disrupt things too much.

[Plotinus]

DeathRowKitty says she's sitting this one out, too. Recruit your friends, we'll start when we have 4 people, which is enough to try out the teams thing.