Sequencer | StrangerCoug's turn

[Micc]

500, 8, 45, 81, 700 to complete the chain for having a factor that is a square number.

[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
  
• [18, 99, 324, 500, 8, 45, 81, 700] {
  k² | n; k > 1
  } numbers with a factor that is a square number

Analysis (Not_Mafia, Micc) has 84 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
  
• [17, 33, 73] {
  n ≡ 1 (mod 8)
  } numbers that are congruent to 1 mod 8

Cards left in deck: 95

It is

skitter30's

turn

[skitter30]

@plot i think you completed the wrong sequence for micc; he completed 'numbers with a factor that is a square', not 'square numbers'

i play 1, 10, 23 as numbers that when converted to number of days in the year would be in the month of january

(i.e. 1 is jan 1st; 10 is jan 10th; 32 would be february 1st, 33 would be february 2nd, and so on)

[Not_Mafia]

That's just a roundabout way of saying numbers under 30

[Not_Mafia]

31*

[skitter30]

That is true

[StrangerCoug]

@plot i think you completed the wrong sequence for micc; he completed 'numbers with a factor that is a square', not 'square numbers'

Further, only 81 is itself a square

[Plotinus]

You're right, I did. I remember looking carefully at both of those sequences and trying to pick the right one and still got it wrong. Fixed it, I hope.

We recently discussed numbers less than 27 and ruled against it for being uninteresting / not having something meaningful in common. Does framing "n <= 31" in terms of days of the year make it interesting enough to rule this one differently?

I think some day of the year sequences could be interesting, like intercalary days, prime days of prime months, palindromic dates, [nationality] name days for names starting with [letter]. Months with 31 days would have a stronger case for being interesting than January but would also be easier to steal.

[StrangerCoug]

We recently discussed numbers less than 27 and ruled against it for being uninteresting / not having something meaningful in common. Does framing "n <= 31" in terms of days of the year make it interesting enough to rule this one differently?

I think some day of the year sequences could be interesting, like intercalary days, prime days of prime months, palindromic dates, [nationality] name days for names starting with [letter]. Months with 31 days would have a stronger case for being interesting than January but would also be easier to steal.

I'm cold about allowing the current rule for the same reason you describe, but I do like the idea of date-based sequences in principle. We could use a deck in Game 3 that is amenable to that.

[skitter30]

ok
60 to numbers that end in 0

[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
  
• [18, 99, 324, 500, 8, 45, 81, 700] {
  k² | n; k > 1
  } numbers with a factor that is a square number

Analysis (Not_Mafia, Micc) has 84 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, 60] {
  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
  
• [17, 33, 73] {
  n ≡ 1 (mod 8)
  } numbers that are congruent to 1 mod 8

Cards left in deck: 94

It is

Not_Mafia's

turn

[Not_Mafia]

Play

15, 17, 1, 1000, 18

as numbers starting in 1

[Plotinus]

Strangercoug has submitted his turn by PM, ironically beating somebody else to the punch:

Complete the squares with 256, 400, 529, and 841 if I'm not unlucky enough to be beaten to the punch again.

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
  
• [18, 99, 324, 500, 8, 45, 81, 700] {
  k² | n; k > 1
  } numbers with a factor that is a square number
  
• [25, 49, 100, 256, 400, 529, 841] {
  n²
  } square numbers

Analysis (Not_Mafia, Micc) has 84 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, 60] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero
  
• [1, 15, 17, 18, 1000] {
  n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with one

Algebra (StrangerCoug, skitter30) has 52 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
  
• [17, 33, 73] {
  n ≡ 1 (mod 8)
  } numbers that are congruent to 1 mod 8

Cards left in deck: 81

It is

Micc's

turn

[Micc]

1, 11, 16, 19 onto numbers where first digit is 1.

[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
  
• [18, 99, 324, 500, 8, 45, 81, 700] {
  k² | n; k > 1
  } numbers with a factor that is a square number
  
• [25, 49, 100, 256, 400, 529, 841] {
  n²
  } square numbers
  
• [1, 15, 17, 18, 1000, 11, 16, 19] {
  n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with one

Analysis (Not_Mafia, Micc) has 92 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, 60] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero

Algebra (StrangerCoug, skitter30) has 52 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
  
• [17, 33, 73] {
  n ≡ 1 (mod 8)
  } numbers that are congruent to 1 mod 8

Cards left in deck: 78

It is

skitter30's

turn

There's already a 1 in the sequence, so you keep that card. Since this still completes the sequence you just get 8 points instead of 9

[Micc]

I should really pay more attention to that rule. Sorry!

[skitter30]

10, 23, 36, 49 as numbers congruent to 10 mod 13

[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
  
• [18, 99, 324, 500, 8, 45, 81, 700] {
  k² | n; k > 1
  } numbers with a factor that is a square number
  
• [25, 49, 100, 256, 400, 529, 841] {
  n²
  } square numbers
  
• [1, 15, 17, 18, 1000, 11, 16, 19] {
  n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with one

Analysis (Not_Mafia, Micc) has 92 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, 60] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero

Algebra (StrangerCoug, skitter30) has 52 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
  
• [17, 33, 73] {
  n ≡ 1 (mod 8)
  } numbers that are congruent to 1 mod 8
  
• [10, 23, 36, 49] {
  n ≡ 10 (mod 13)
  } numbers congruent to 10 mod 13

Cards left in deck: 78

It is

Not_Mafia's

turn

[Not_Mafia]

729, 1 to numbers that congruent to 1 mod 8

[Plotinus]

You don't have a 1. You can resubmit your turn

[skitter30]

[10, 23, 36, 59] { n ≡ 10 (mod 13) } numbers congruent to 10 mod 13

the 59 ought to be a 49

[Plotinus]

fixed

[Not_Mafia]

You don't have a 1. You can resubmit your turn

Add just the 729

[Plotinus]

StrangerCoug has submitted his turn by PM:

Play 20, 800, 1000 to finish the numbers ending in 0.

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
  
• [18, 99, 324, 500, 8, 45, 81, 700] {
  k² | n; k > 1
  } numbers with a factor that is a square number
  
• [25, 49, 100, 256, 400, 529, 841] {
  n²
  } square numbers
  
• [1, 15, 17, 18, 1000, 11, 16, 19] {
  n = 1 * 10^d + a₀10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that start with one
  
• [10, 40, 600, 60, 20, 800, 1000] {
  n = 10 * a₀*10^d + a₁10^d-1 + ... + a_d-110⁰ with a_i, d ≥ 0
  } numbers that end with zero

Analysis (Not_Mafia, Micc) has 92 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

Algebra (StrangerCoug, skitter30) has 59 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
  
• [17, 33, 73, 729] {
  n ≡ 1 (mod 8)
  } numbers that are congruent to 1 mod 8
  
• [10, 23, 36, 49] {
  n ≡ 10 (mod 13)
  } numbers congruent to 10 mod 13

Cards left in deck: 74

It is

Micc's

turn

[Micc]

83, 89, and 400 for their first digit being a power of 2.