Sequencer | StrangerCoug's turn

[Not_Mafia]

Play 512, 52, 24 to numbers where at least one digit is a 2

[Plotinus]

StrangerCoug has submitted his turn by PM:

Play 100, 50, 35, and 250 to complete the multiples of 5 if it's still there on my turn.

Spoiler: Completed sequences

• [1, 2, 3, 4, 5, 10, 39, 55] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
  } numbers that are divisible by their first digit
  
• [6, 21, 27, 42, 69, 72, 78, 165, 576] {
  3n
  } numbers whose sum is a multiple of 3
  
• [4, 8, 9, 15, 20, 32, 66, 80] {
  n = 2ⁱ ± 2^j
  } numbers that can be written as the sum or difference of two powers of two
  
• [20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
  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 }
  
• [16, 20, 25, 32, 94, 120, 200] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
  } composite numbers whose digit sum is prime
  
• [1, 3, 4, 5, 6, 7, 9] {
  n < 10
  } single digit numbers }
  
• [3, 5, 16, 17, 25, 64, 128, 729] {
  p^k, p is prime, k ≥ 1
  } powers of primes (1st and higher)
  
• [12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
  
• [10, 88, 90, 97, 100, 225, 441] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
  } digit sum is a perfect square
  
• [1, 2, 3, 7, 9 11, 77]{
  str(n)[::-1] == str(n)
  } Palindromic numbers
  
• [84, 56, 3, 29, 93, 5, 70] {
  n % 9 ∈ {2, 3, 5, 7}
  Numbers who digital root is prime
  
• [22, 3, 8, 65, 51, 64, 12] {
  i % (i % 10) == 0 }
  Numbers divisible by their last digit
  
• [12, 20, 21, 27, 512, 52, 24] {
  n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
  } Numbers where at least one digit is 2
  
• [15, 50, 75, 100, 50, 35, 250] {
  5n
  } numbers that are evenly divisible by 5

Analysis (Not_Mafia, Micc) has 61 points and:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [13, 35, 300] contains a treble letter when written in Roman numerals
  
• [91, 900, 961] {
  n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with nine
  
• [10, 40, 600] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero

Algebra (StrangerCoug, Jackal711) has 45 points and:

• [19, 46, 64, 361] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers whose digit sum equals 10

It is

Micc's

turn

[Plotinus]

Prodded Micc. He has another (expired on 2020-03-11 09:44:47) to go before I start looking for a replacement

[Micc]

bah sorry. i took on way to much at once, but thankfully two games I was moderating recently ended.

I'll play 25, 49, 100 as square numbers.

[Plotinus]

Spoiler: Completed sequences

• [1, 2, 3, 4, 5, 10, 39, 55] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
  } numbers that are divisible by their first digit
  
• [6, 21, 27, 42, 69, 72, 78, 165, 576] {
  3n
  } numbers whose sum is a multiple of 3
  
• [4, 8, 9, 15, 20, 32, 66, 80] {
  n = 2ⁱ ± 2^j
  } numbers that can be written as the sum or difference of two powers of two
  
• [20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
  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 }
  
• [16, 20, 25, 32, 94, 120, 200] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
  } composite numbers whose digit sum is prime
  
• [1, 3, 4, 5, 6, 7, 9] {
  n < 10
  } single digit numbers }
  
• [3, 5, 16, 17, 25, 64, 128, 729] {
  p^k, p is prime, k ≥ 1
  } powers of primes (1st and higher)
  
• [12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
  
• [10, 88, 90, 97, 100, 225, 441] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
  } digit sum is a perfect square
  
• [1, 2, 3, 7, 9 11, 77]{
  str(n)[::-1] == str(n)
  } Palindromic numbers
  
• [84, 56, 3, 29, 93, 5, 70] {
  n % 9 ∈ {2, 3, 5, 7}
  Numbers who digital root is prime
  
• [22, 3, 8, 65, 51, 64, 12] {
  i % (i % 10) == 0 }
  Numbers divisible by their last digit
  
• [12, 20, 21, 27, 512, 52, 24] {
  n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
  } Numbers where at least one digit is 2
  
• [15, 50, 75, 100, 50, 35, 250] {
  5n
  } numbers that are evenly divisible by 5

Analysis (Not_Mafia, Micc) has 61 points and:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [13, 35, 300] contains a treble letter when written in Roman numerals
  
• [91, 900, 961] {
  n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with nine
  
• [10, 40, 600] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero
  
• [25, 49, 100] {
  n²
  } square numbers

Algebra (StrangerCoug, Jackal711) has 45 points and:

• [19, 46, 64, 361] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers whose digit sum equals 10

It is

Jackal711's

turn

[Plotinus]

prodded Jackal711, who has another (expired on 2020-03-12 13:47:55) to go before I start looking for a replacement

[Plotinus]

Jackal has requested replacement due to internet issues. He's hoping to rejoin us in round 3. The scummy this game got created some interest in the game so I have a couple people lined up. We won't have to wait 2 months this time.

[skitter30]

hi i'm replacing jackal

i play 324, 18, 17 as numbers where each successive digit is strictly greater than the previous one

[Plotinus]

skitter30 is replacing jackal711! 324 doesn't seem to obey the rule of that sequence as I understand it, so skitter30 can change their move or re-explain the rule.

[skitter30]

sorry that was some kind of brainfart

324, 18, 33, 99, 60 as numbers divisible by 3

[Plotinus]

Unfortunately we've had an equivalent sequence already, in the completed sequences spoiler:

[6, 21, 27, 42, 69, 72, 78, 165, 576] { 3n } numbers whose sum is a multiple of 3


You can go again, it's okay

[skitter30]

ok third time's the charm:

324, 18, 99 as numbers with a factor that is a square number
i.e. 18 and 99 have 9 as a factor
324 has 9 and 324 as factors

[Plotinus]

Spoiler: Completed sequences

• [1, 2, 3, 4, 5, 10, 39, 55] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
  } numbers that are divisible by their first digit
  
• [6, 21, 27, 42, 69, 72, 78, 165, 576] {
  3n
  } numbers whose sum is a multiple of 3
  
• [4, 8, 9, 15, 20, 32, 66, 80] {
  n = 2ⁱ ± 2^j
  } numbers that can be written as the sum or difference of two powers of two
  
• [20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
  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 }
  
• [16, 20, 25, 32, 94, 120, 200] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
  } composite numbers whose digit sum is prime
  
• [1, 3, 4, 5, 6, 7, 9] {
  n < 10
  } single digit numbers }
  
• [3, 5, 16, 17, 25, 64, 128, 729] {
  p^k, p is prime, k ≥ 1
  } powers of primes (1st and higher)
  
• [12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
  
• [10, 88, 90, 97, 100, 225, 441] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
  } digit sum is a perfect square
  
• [1, 2, 3, 7, 9 11, 77]{
  str(n)[::-1] == str(n)
  } Palindromic numbers
  
• [84, 56, 3, 29, 93, 5, 70] {
  n % 9 ∈ {2, 3, 5, 7}
  Numbers who digital root is prime
  
• [22, 3, 8, 65, 51, 64, 12] {
  i % (i % 10) == 0 }
  Numbers divisible by their last digit
  
• [12, 20, 21, 27, 512, 52, 24] {
  n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
  } Numbers where at least one digit is 2
  
• [15, 50, 75, 100, 50, 35, 250] {
  5n
  } numbers that are evenly divisible by 5

Analysis (Not_Mafia, Micc) has 61 points and:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [13, 35, 300] contains a treble letter when written in Roman numerals
  
• [91, 900, 961] {
  n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with nine
  
• [10, 40, 600] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero
  
• [25, 49, 100] {
  n²
  } square numbers

Algebra (StrangerCoug, skitter30) has 45 points and:

• [19, 46, 64, 361] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers whose digit sum equals 10
  
• [18, 99, 324] {
  k² | n; k ∈ ℤ
  } numbers with a factor that is a square number

It is

Not_Mafia's

turn

That did it! It's hard jumping in midstream, thanks for joining us.

[Not_Mafia]

Doesn't every number have a factor that is a square number as 1 is a square number, or am I mathsing wrong?

[Not_Mafia]

Play entire hand on "numbers with a factor that is a square number", if that's not a valid move then add 28 to the roman numerals

[Plotinus]

For the sake of interestingness, let's limit skitter's sequence to factors greater than one.

Strangercoug has submitted his turn by PM

6, 15, 44: Numbers divisible by each of its digits

Spoiler: Completed sequences

• [1, 2, 3, 4, 5, 10, 39, 55] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
  } numbers that are divisible by their first digit
  
• [6, 21, 27, 42, 69, 72, 78, 165, 576] {
  3n
  } numbers whose sum is a multiple of 3
  
• [4, 8, 9, 15, 20, 32, 66, 80] {
  n = 2ⁱ ± 2^j
  } numbers that can be written as the sum or difference of two powers of two
  
• [20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
  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 }
  
• [16, 20, 25, 32, 94, 120, 200] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
  } composite numbers whose digit sum is prime
  
• [1, 3, 4, 5, 6, 7, 9] {
  n < 10
  } single digit numbers }
  
• [3, 5, 16, 17, 25, 64, 128, 729] {
  p^k, p is prime, k ≥ 1
  } powers of primes (1st and higher)
  
• [12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
  
• [10, 88, 90, 97, 100, 225, 441] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
  } digit sum is a perfect square
  
• [1, 2, 3, 7, 9 11, 77]{
  str(n)[::-1] == str(n)
  } Palindromic numbers
  
• [84, 56, 3, 29, 93, 5, 70] {
  n % 9 ∈ {2, 3, 5, 7}
  Numbers who digital root is prime
  
• [22, 3, 8, 65, 51, 64, 12] {
  i % (i % 10) == 0 }
  Numbers divisible by their last digit
  
• [12, 20, 21, 27, 512, 52, 24] {
  n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
  } Numbers where at least one digit is 2
  
• [15, 50, 75, 100, 50, 35, 250] {
  5n
  } numbers that are evenly divisible by 5

Analysis (Not_Mafia, Micc) has 61 points and:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [13, 28, 35, 300] contains a treble letter when written in Roman numerals
  
• [91, 900, 961] {
  n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with nine
  
• [10, 40, 600] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero
  
• [25, 49, 100] {
  n²
  } square numbers

Algebra (StrangerCoug, skitter30) has 45 points and:

• [19, 46, 64, 361] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers whose digit sum equals 10
  
• [18, 99, 324] {
  k² | n; k > 1
  } numbers with a factor that is a square number
  
• [6, 15, 44] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
  } Numbers divisible by each of its digits

Cards left in deck: 112

It is

Micc's

turn

[Micc]

98, 28, 343, 63, 289 to complete triple letters when written in roman numerals.

[Plotinus]

I had two submissions by PM from other players who wanted to complete that sequence. Good job, Micc!

Spoiler: Completed sequences

• [1, 2, 3, 4, 5, 10, 39, 55] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
  } numbers that are divisible by their first digit
  
• [6, 21, 27, 42, 69, 72, 78, 165, 576] {
  3n
  } numbers whose sum is a multiple of 3
  
• [4, 8, 9, 15, 20, 32, 66, 80] {
  n = 2ⁱ ± 2^j
  } numbers that can be written as the sum or difference of two powers of two
  
• [20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
  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 }
  
• [16, 20, 25, 32, 94, 120, 200] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
  } composite numbers whose digit sum is prime
  
• [1, 3, 4, 5, 6, 7, 9] {
  n < 10
  } single digit numbers }
  
• [3, 5, 16, 17, 25, 64, 128, 729] {
  p^k, p is prime, k ≥ 1
  } powers of primes (1st and higher)
  
• [12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
  
• [10, 88, 90, 97, 100, 225, 441] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
  } digit sum is a perfect square
  
• [1, 2, 3, 7, 9 11, 77]{
  str(n)[::-1] == str(n)
  } Palindromic numbers
  
• [84, 56, 3, 29, 93, 5, 70] {
  n % 9 ∈ {2, 3, 5, 7}
  Numbers who digital root is prime
  
• [22, 3, 8, 65, 51, 64, 12] {
  i % (i % 10) == 0 }
  Numbers divisible by their last digit
  
• [12, 20, 21, 27, 512, 52, 24] {
  n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
  } Numbers where at least one digit is 2
  
• [15, 50, 75, 100, 50, 35, 250] {
  5n
  } numbers that are evenly divisible by 5
  
• [13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals

Analysis (Not_Mafia, Micc) has 69 points and:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [91, 900, 961] {
  n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with nine
  
• [10, 40, 600] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero
  
• [25, 49, 100] {
  n²
  } square numbers

Algebra (StrangerCoug, skitter30) has 45 points and:

• [19, 46, 64, 361] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers whose digit sum equals 10
  
• [18, 99, 324] {
  k² | n; k > 1
  } numbers with a factor that is a square number
  
• [6, 15, 44] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
  } Numbers divisible by each of its digits

Cards left in deck: 107

It is

skitter30's

turn

[skitter30]

17, 33, 73 as numbers that are congruent to 1 mod 8

[Not_Mafia]

Play entire hand on "numbers with a factor that is a square number", if that's not a valid move then add 28 to the roman numerals

98, 28, 343, 63, 289 to complete triple letters when written in roman numerals.

28 is a duplicate here

[Plotinus]

Spoiler: Completed sequences

• [1, 2, 3, 4, 5, 10, 39, 55] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
  } numbers that are divisible by their first digit
  
• [6, 21, 27, 42, 69, 72, 78, 165, 576] {
  3n
  } numbers whose sum is a multiple of 3
  
• [4, 8, 9, 15, 20, 32, 66, 80] {
  n = 2ⁱ ± 2^j
  } numbers that can be written as the sum or difference of two powers of two
  
• [20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
  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 }
  
• [16, 20, 25, 32, 94, 120, 200] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
  } composite numbers whose digit sum is prime
  
• [1, 3, 4, 5, 6, 7, 9] {
  n < 10
  } single digit numbers }
  
• [3, 5, 16, 17, 25, 64, 128, 729] {
  p^k, p is prime, k ≥ 1
  } powers of primes (1st and higher)
  
• [12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
  
• [10, 88, 90, 97, 100, 225, 441] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
  } digit sum is a perfect square
  
• [1, 2, 3, 7, 9 11, 77]{
  str(n)[::-1] == str(n)
  } Palindromic numbers
  
• [84, 56, 3, 29, 93, 5, 70] {
  n % 9 ∈ {2, 3, 5, 7}
  Numbers who digital root is prime
  
• [22, 3, 8, 65, 51, 64, 12] {
  i % (i % 10) == 0 }
  Numbers divisible by their last digit
  
• [12, 20, 21, 27, 512, 52, 24] {
  n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
  } Numbers where at least one digit is 2
  
• [15, 50, 75, 100, 50, 35, 250] {
  5n
  } numbers that are evenly divisible by 5
  
• [13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals

Analysis (Not_Mafia, Micc) has 69 points and:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [91, 900, 961] {
  n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with nine
  
• [10, 40, 600] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero
  
• [25, 49, 100] {
  n²
  } square numbers

Algebra (StrangerCoug, skitter30) has 45 points and:

• [19, 46, 64, 361] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers whose digit sum equals 10
  
• [18, 99, 324] {
  k² | n; k > 1
  } numbers with a factor that is a square number
  
• [6, 15, 44] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
  } Numbers divisible by each of its digits
  
• [17, 33, 73] {
  n ≡ 1 (mod 8)
  } numbers that are congruent to 1 mod 8

Cards left in deck: 105

It is

Not_Mafia's

turn

Play entire hand on "numbers with a factor that is a square number", if that's not a valid move then add 28 to the roman numerals

98, 28, 343, 63, 289 to complete triple letters when written in roman numerals.

28 is a duplicate here

Fixed, I've removed a point and the 28 from the list. I've already given Micc his new cards but I'll reshuffle that 28 back into the deck so it can be drawn again.

[Not_Mafia]

Add 1, 36, 55, 4 to numbers divisible by each of its digits

[Plotinus]

Spoiler: Completed sequences

• [1, 2, 3, 4, 5, 10, 39, 55] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
  } numbers that are divisible by their first digit
  
• [6, 21, 27, 42, 69, 72, 78, 165, 576] {
  3n
  } numbers whose sum is a multiple of 3
  
• [4, 8, 9, 15, 20, 32, 66, 80] {
  n = 2ⁱ ± 2^j
  } numbers that can be written as the sum or difference of two powers of two
  
• [20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
  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 }
  
• [16, 20, 25, 32, 94, 120, 200] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
  } composite numbers whose digit sum is prime
  
• [1, 3, 4, 5, 6, 7, 9] {
  n < 10
  } single digit numbers }
  
• [3, 5, 16, 17, 25, 64, 128, 729] {
  p^k, p is prime, k ≥ 1
  } powers of primes (1st and higher)
  
• [12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
  
• [10, 88, 90, 97, 100, 225, 441] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
  } digit sum is a perfect square
  
• [1, 2, 3, 7, 9 11, 77]{
  str(n)[::-1] == str(n)
  } Palindromic numbers
  
• [84, 56, 3, 29, 93, 5, 70] {
  n % 9 ∈ {2, 3, 5, 7}
  Numbers who digital root is prime
  
• [22, 3, 8, 65, 51, 64, 12] {
  i % (i % 10) == 0 }
  Numbers divisible by their last digit
  
• [12, 20, 21, 27, 512, 52, 24] {
  n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
  } Numbers where at least one digit is 2
  
• [15, 50, 75, 100, 50, 35, 250] {
  5n
  } numbers that are evenly divisible by 5
  
• [13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
  
• [6, 15, 44, 1, 36, 55, 4] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
  } Numbers divisible by each of its digits

Analysis (Not_Mafia, Micc) has 76 points and:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [91, 900, 961] {
  n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with nine
  
• [10, 40, 600] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero
  
• [25, 49, 100] {
  n²
  } square numbers

Algebra (StrangerCoug, skitter30) has 45 points and:

• [19, 46, 64, 361] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers whose digit sum equals 10
  
• [18, 99, 324] {
  k² | n; k > 1
  } numbers with a factor that is a square number
  
• [17, 33, 73] {
  n ≡ 1 (mod 8)
  } numbers that are congruent to 1 mod 8

Cards left in deck: 101

It is

StrangerCoug's

turn

[StrangerCoug]

Add 56 to the numbers that end in 6

[Plotinus]

Spoiler: Completed sequences

• [1, 2, 3, 4, 5, 10, 39, 55] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a₀ | n; a_i ≥ 0; d > 0
  } numbers that are divisible by their first digit
  
• [6, 21, 27, 42, 69, 72, 78, 165, 576] {
  3n
  } numbers whose sum is a multiple of 3
  
• [4, 8, 9, 15, 20, 32, 66, 80] {
  n = 2ⁱ ± 2^j
  } numbers that can be written as the sum or difference of two powers of two
  
• [20, 35, 79, 169, 8, 53, 2, 35, 13 ] {
  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 }
  
• [16, 20, 25, 32, 94, 120, 200] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is prime; φ(n) < n - 1; a_i ≥ 0, d > 0; k ∈ ℤ
  } composite numbers whose digit sum is prime
  
• [1, 3, 4, 5, 6, 7, 9] {
  n < 10
  } single digit numbers }
  
• [3, 5, 16, 17, 25, 64, 128, 729] {
  p^k, p is prime, k ≥ 1
  } powers of primes (1st and higher)
  
• [12, 34, 48, 729, 86, 81, 64, 24] numbers that have two or more tall letters (b, d, f, h, k, l, t) when written as a word.
  
• [10, 88, 90, 97, 100, 225, 441] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = m²; a_i ≥ 0, d, m > 0; k ∈ ℤ
  } digit sum is a perfect square
  
• [1, 2, 3, 7, 9 11, 77]{
  str(n)[::-1] == str(n)
  } Palindromic numbers
  
• [84, 56, 3, 29, 93, 5, 70] {
  n % 9 ∈ {2, 3, 5, 7}
  Numbers who digital root is prime
  
• [22, 3, 8, 65, 51, 64, 12] {
  i % (i % 10) == 0 }
  Numbers divisible by their last digit
  
• [12, 20, 21, 27, 512, 52, 24] {
  n = a * 100 + b * 10 + c, with 2 ∈ {a, b, c}
  } Numbers where at least one digit is 2
  
• [15, 50, 75, 100, 50, 35, 250] {
  5n
  } numbers that are evenly divisible by 5
  
• [13, 28, 35, 300, 98 343, 63, 289] contains a treble letter when written in Roman numerals
  
• [6, 15, 44, 1, 36, 55, 4] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i | n
  } Numbers divisible by each of its digits

Analysis (Not_Mafia, Micc) has 76 points and:

• [16, 56, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [91, 900, 961] {
  n = 9*10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with nine
  
• [10, 40, 600] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero
  
• [25, 49, 100] {
  n²
  } square numbers

Algebra (StrangerCoug, skitter30) has 45 points and:

• [19, 46, 64, 361] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers whose digit sum equals 10
  
• [18, 99, 324] {
  k² | n; k > 1
  } numbers with a factor that is a square number
  
• [17, 33, 73] {
  n ≡ 1 (mod 8)
  } numbers that are congruent to 1 mod 8

Cards left in deck: 100

It is

Micc's

turn