Sequencer | StrangerCoug's turn

[DeathRowKitty]

[3, 54, 80] numbers n for which there exists some positive integer with exactly 2n primitive roots

27 has 2*3 = 6 primitive roots
379 has 2*54 = 108 primitive roots
401 has 2*80 = 160 primitive roots

[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

McMenno is inactive:

Implosion has 28 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 30 points and:

• [38, 82, 84] slots never touched by Ace, 5, or 9 in perfect out-shuffles of standard 52 card decks, mod 52
  
• [3, 54, 80] numbers n for which there exists some positive integer with exactly 2n primitive roots

Felissan has 21 points and:

• [2, 4, 32, 256] {
  2ⁿ
  } powers of two
  
• [30, 40, 55] {
  25 + (5n * (n + 1) / 2)
  } 25 + 5n, where n is a triangular number

popsofctown has 14 points and:

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

StrangerCoug has 14 points and:

• [13, 27, 72] {
  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

There are 44 cards left in the deck. It is Felissan's turn.

[Plotinus]

Felissan has been prodded. It will be popsofctown's turn in (expired on 2019-11-02 02:35:57) or as soon as Felissan goes, whichever happens first.

[Plotinus]

popsofctown has been prodded. It will be StrangerCoug's turn in (expired on 2019-11-04 02:52:32) or as soon as popsofctown goes, whichever happens first.

[popsofctown]

Pass

[StrangerCoug]

Add 5 to triangular numbers + 4

[implosion]

Eh shrug sure.

Numbers where each pair of consecutive digits differs by exactly one: 2, 3, 23, 56.

[DeathRowKitty]

Add [1, 6, 26, 220] to primitive roots sequence

5 has 2*1 = 2 primitive roots
29 has 2*6 = 12 primitive roots
107 has 2*26 = 52 primitive roots
1331 has 2*220 = 440 primitive roots


I had far too much fun playing around with this sequence tbh and didn't even check if there's another sequence I could/should be completing instead.

[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

McMenno is inactive:

Implosion has 28 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).
  
• [2, 3, 23, 56] Numbers where each pair of consecutive digits differ by exactly one

DeathRowKitty has 37 points and:

• [38, 82, 84] slots never touched by Ace, 5, or 9 in perfect out-shuffles of standard 52 card decks, mod 52

Felissan has 21 points and:

• [2, 4, 32, 256] {
  2ⁿ
  } powers of two
  
• [30, 40, 55] {
  25 + (5n * (n + 1) / 2)
  } 25 + 5n, where n is a triangular number

popsofctown has 14 points and:

• [4, 20, 36, 68] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [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

StrangerCoug has 14 points and:

• [13, 27, 72] {
  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
  
• [5, 7, 10, 14] {
  n*(n-1)/2) + 4
  } triangular numbers + 4

There are 35 cards left in the deck. It is Felissan's turn.

[Felissan]

I play [3, 39, 165] as multiples of 3.

[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

McMenno is inactive:

Implosion has 28 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).
  
• [2, 3, 23, 56] Numbers where each pair of consecutive digits differ by exactly one

DeathRowKitty has 37 points and:

• [38, 82, 84] slots never touched by Ace, 5, or 9 in perfect out-shuffles of standard 52 card decks, mod 52

Felissan has 21 points and:

• [2, 4, 32, 256] {
  2ⁿ
  } powers of two
  
• [30, 40, 55] {
  25 + (5n * (n + 1) / 2)
  } 25 + 5n, where n is a triangular number
  
• [3, 39, 165] {
  3n
  } multipes of 3

popsofctown has 14 points and:

• [4, 20, 36, 68] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [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

StrangerCoug has 14 points and:

• [13, 27, 72] {
  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
  
• [5, 7, 10, 14] {
  n*(n-1)/2) + 4
  } triangular numbers + 4

There are 32 cards left in the deck. It is popsofctown's turn.

[popsofctown]

such a fast game

let's see if I can outscore cougar face

I blame him for losing that dumb multiball setup I should vindicate my grudge with the power of numbers

[popsofctown]

I feel :/ about having to skip my turn because I only had 24 hours and had a needed night of sleep and a plane flight in that window

need to catch up

[popsofctown]

I don't really like/under/see the point of adding a single entry to someone else's sequence "stealing" the sequence.

Like the rules as is don't give the person the sequence "belongs" to any advantage, right? It is equally allowed to finish your own sequence or steal and finish someone else's sequence. So if you're going to list unfinished sequences and associate them with someone's name I would prefer to them to be associated with the author of the sequence. It's like, just more fun. I want to be angry at DRK about hurting my brain about outshuffles even if someone adds 1 number to it. And I want to see the full portfolio of what a troll implosion is all in one place.


But maybe I just don't understand the rules to this game because DRK has a number of points that's not divisible by 7 and I don't even know how that's possible

[popsofctown]

I add 75 to Felissan's 25+5n sequence.

[DeathRowKitty]

I want to be angry at DRK about hurting my brain about outshuffles even if someone adds 1 number to it. And I want to see the full portfolio of what a troll implosion is all in one place.

Aw, you don't need that sequence to be angry at me! I'll tell you what...if someone steals that one, I'll try to come up with something far more obnoxious so you don't forget to be mad, okay? <3


As for the points thing, I have a number of points not divisible by 7 because I completed a sequence with 9 cards and you get 1 point for each card in a sequence you complete.

[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

McMenno is inactive:

Implosion has 28 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).
  
• [2, 3, 23, 56] Numbers where each pair of consecutive digits differ by exactly one

DeathRowKitty has 37 points and:

• [38, 82, 84] slots never touched by Ace, 5, or 9 in perfect out-shuffles of standard 52 card decks, mod 52

Felissan has 21 points and:

• [2, 4, 32, 256] {
  2ⁿ
  } powers of two
  
• [3, 39, 165] {
  3n
  } multipes of 3

popsofctown has 14 points and:

• [4, 20, 36, 68] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [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

StrangerCoug has 14 points and:

• [13, 27, 72] {
  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
  
• [5, 7, 10, 14] {
  n*(n-1)/2) + 4
  } triangular numbers + 4

There are 31 cards left in the deck. It is StrangerCoug's turn.

[Plotinus]

I don't really like/under/see the point of adding a single entry to someone else's sequence "stealing" the sequence.

Like the rules as is don't give the person the sequence "belongs" to any advantage, right? It is equally allowed to finish your own sequence or steal and finish someone else's sequence. So if you're going to list unfinished sequences and associate them with someone's name I would prefer to them to be associated with the author of the sequence. It's like, just more fun. I want to be angry at DRK about hurting my brain about outshuffles even if someone adds 1 number to it. And I want to see the full portfolio of what a troll implosion is all in one place.


But maybe I just don't understand the rules to this game because DRK has a number of points that's not divisible by 7 and I don't even know how that's possible

Yeah, the stealing mechanic needs some more work. You're right that the way things are now, it's pretty cosmetic whose name the sequence is printed after, since all that matters for points is who has it last.

One thing that might be interesting when we do teams is each team could have a colour and i'd put the numbers in that team's colour, so you could see that [

72, 256, 800

,

2304, 5184

,

16, 729

] was started by team red, stolen by team blue, and completed by team indigo. It's cosmetic but then we could just leave the sequences by the original person's name until they're completed.

[StrangerCoug]

Add 24 to the multiples of 3

[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

McMenno is inactive:

Implosion has 28 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).
  
• [2, 3, 23, 56] Numbers where each pair of consecutive digits differ by exactly one

DeathRowKitty has 37 points and:

• [38, 82, 84] slots never touched by Ace, 5, or 9 in perfect out-shuffles of standard 52 card decks, mod 52

Felissan has 21 points and:

• [2, 4, 32, 256] {
  2ⁿ
  } powers of two

popsofctown has 14 points and:

• [4, 20, 36, 68] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [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

StrangerCoug has 14 points and:

• [13, 27, 72] {
  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
  
• [5, 7, 10, 14] {
  n*(n-1)/2) + 4
  } triangular numbers + 4
  
• [3, 24, 39, 165] {
  3n
  } multiples of 3

There are 30 cards left in the deck. It is implosion's turn.

[implosion]

finish numbers whose digit sum is a square with 97, 88, 18, 4.

[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

McMenno is inactive:

Implosion has 35 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).
  
• [2, 3, 23, 56] Numbers where each pair of consecutive digits differ by exactly one

DeathRowKitty has 37 points and:

• [38, 82, 84] slots never touched by Ace, 5, or 9 in perfect out-shuffles of standard 52 card decks, mod 52

Felissan has 21 points and:

• [2, 4, 32, 256] {
  2ⁿ
  } powers of two

popsofctown has 14 points and:

• [4, 20, 36, 68] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [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

StrangerCoug has 14 points and:

• [5, 7, 10, 14] {
  n*(n-1)/2) + 4
  } triangular numbers + 4
  
• [3, 24, 39, 165] {
  3n
  } multiples of 3

There are 26 cards left in the deck. It is DeathRowKitty's turn.

[DeathRowKitty]

Add [21, 33, 84] to multiples of 3

[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

McMenno is inactive:

Implosion has 35 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).
  
• [2, 3, 23, 56] Numbers where each pair of consecutive digits differ by exactly one

DeathRowKitty has 44 points and:

• [38, 82, 84] slots never touched by Ace, 5, or 9 in perfect out-shuffles of standard 52 card decks, mod 52

Felissan has 21 points and:

• [2, 4, 32, 256] {
  2ⁿ
  } powers of two

popsofctown has 14 points and:

• [4, 20, 36, 68] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [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

StrangerCoug has 14 points and:

• [5, 7, 10, 14] {
  n*(n-1)/2) + 4
  } triangular numbers + 4

There are 23 cards left in the deck. It is Felissan's turn.

[Plotinus]

Since McMenno is probably not coming back, should i add his hand to the bottom of the deck?