Sequencer | StrangerCoug's turn

[StrangerCoug]

Could I be PM'd an updated hand, please? I can't find it.

[Plotinus]

I have only just now sent StrangerCoug his hand, so his 48 hours start now.

[StrangerCoug]

69. 99, 269: Numbers that contain a 9

[Plotinus]

Spoiler: completed sequences

• [54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
  
• [78, 126, 336, 348, 192, 315, 123] {
  n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
  } composite numbers whose digit sum is composite
  
• [55, 226, 253, 190, 19, 352, 334] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
  } numbers whose digit sum equals 10
  
• [3, 7, 229, 5, 179, 17, 137] primes
  
• [25, 44, 63, 365, 52, 62, 88, 175] {
  i % (i % 10) == 0
  } Numbers divisible by their last digit
  
• [166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
  
• [1, 4, 43, 141, 301, 302, 341] have four or fewer factors
  
• [90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
  
• [234, 342, 356, 140, 173, 200, 280, 299] {
  n = 100×a + 10×b + c with c < a + b
  } 3 digit numbers where the last digit is less than the sum of the first two digits
  
• [39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
  
• [174, 118, 274, 232, 316, 180, 358 ] {
  2 | n ∧ n ≥ 100
  } 3 digit even numbers
  
• [48, 135, 306, 40, 84, 132, 243] {
  k² | n, k > 1
  } numbers that are divisible by a perfect square greater than one
  
• [235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
  
• [125, 270, 320, 30, 45, 100, 150] {
  2ⁱ×3^j×5^k with i, j, k ≥ 0
  } 5-smooth numbers
  
• [202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
  
• [120, 143, 194, 8, 15, 98, 170] {
  n ∈ [k² - 2, k² + 2], k ∈ ℤ
  numbers within 2 of a perfect square
  
• [191, 359, 305, 271, 199, 163, 109] {
  n > 100 ∧ n % 2 = 1
  } 3 digit odd numbers
  
• [128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
  
• [116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
  
• [16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
  
• [95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
  
• [37, 53, 75, 339, 9, 57, 197] all digits are odd
  
• [220, 162, 18, 42, 107, 201, 213, 230]
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers where the sum of the digits is a single digit
  
• [121, 209, 252, 29, 67, 92, 119 ] {
  (n(n+1)/2 + 1) or (n(n+1)/2 - 1)
  } numbers that are exactly one away from a triangular number
  
• [134, 146, 238, 248, 145, 139, 236] {
  n = 100*a + 10*b + c with 0 < a < b < c < 10
  } 3 digit numbers whose digits are in strictly ascending order
  
• [176, 298, 295, 251, 330, 258, and 211] {
  n = 100*a + 10*b + c, b is odd
  } 3 digit numbers where the middle digit is odd
  
• [20, 56, 60, 85, 36, 41, 66, 79, 82] {
  9 < n < 100
  2 digit numbers
  
• [361, 283, 343, 223, 241, 355, 331, 91] {
  n ≡ 1 (mod 6)
  } (multiples of 6) + 1
  
• [105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
  
• [244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
  
• [347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
  
• [65, 345 285, 240, 160, 70, 225] {
  5 | n
  } multiples of 5
  
• [47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
  
• [80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
  
• [102, 366, 87, 108, 198, 264, 159] {
  3 | n
  } multiplies of 3
  
• [73, 157, 231, 35, 111, 72, 101] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
  } Numbers none of whose digits are composite
  
• [318, 266, 208, 154, 64, 6, 350] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
  } Even numbers whose digit sum is also even

Topology: Micc, Not_Mafia: 89 points

• [171, 323, 77] palindromes
  
• [249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

• [46, 59, 164] {
  n ≡ ±1 (mod 15)
  } numbers equivalent to ±1 mod 15
  
• [286, 207, 349] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
  } Numbers whose digit sum is a perfect square
  
• [23, 293, 161] {
  n ≡ 5 (mod 6)
  } numbers equivalent to 5 mod 6
  
• [69. 99, 269] numbers that contain a 9

Dynamics: lilith2013, skitter30: 99 points

• [328, 28, 276, 275] numbers that contain a 27 or 28
  
• [124, 214, 282] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers that consist only of digits that are powers of 2 (including 1)
  
• [81, 189, 324, 27, 297] {
  27 | n
  } multiples of 27

It is

ilith2013

's turn.

There are 22 cards remaining

[lilith2013]

Please let me know if this isn't a valid sequence:

Play 360, 152, 265 as

numbers whose second digit from the right is the largest digit

[Plotinus]

Spoiler: completed sequences

• [54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
  
• [78, 126, 336, 348, 192, 315, 123] {
  n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
  } composite numbers whose digit sum is composite
  
• [55, 226, 253, 190, 19, 352, 334] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
  } numbers whose digit sum equals 10
  
• [3, 7, 229, 5, 179, 17, 137] primes
  
• [25, 44, 63, 365, 52, 62, 88, 175] {
  i % (i % 10) == 0
  } Numbers divisible by their last digit
  
• [166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
  
• [1, 4, 43, 141, 301, 302, 341] have four or fewer factors
  
• [90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
  
• [234, 342, 356, 140, 173, 200, 280, 299] {
  n = 100×a + 10×b + c with c < a + b
  } 3 digit numbers where the last digit is less than the sum of the first two digits
  
• [39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
  
• [174, 118, 274, 232, 316, 180, 358 ] {
  2 | n ∧ n ≥ 100
  } 3 digit even numbers
  
• [48, 135, 306, 40, 84, 132, 243] {
  k² | n, k > 1
  } numbers that are divisible by a perfect square greater than one
  
• [235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
  
• [125, 270, 320, 30, 45, 100, 150] {
  2ⁱ×3^j×5^k with i, j, k ≥ 0
  } 5-smooth numbers
  
• [202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
  
• [120, 143, 194, 8, 15, 98, 170] {
  n ∈ [k² - 2, k² + 2], k ∈ ℤ
  numbers within 2 of a perfect square
  
• [191, 359, 305, 271, 199, 163, 109] {
  n > 100 ∧ n % 2 = 1
  } 3 digit odd numbers
  
• [128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
  
• [116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
  
• [16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
  
• [95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
  
• [37, 53, 75, 339, 9, 57, 197] all digits are odd
  
• [220, 162, 18, 42, 107, 201, 213, 230]
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers where the sum of the digits is a single digit
  
• [121, 209, 252, 29, 67, 92, 119 ] {
  (n(n+1)/2 + 1) or (n(n+1)/2 - 1)
  } numbers that are exactly one away from a triangular number
  
• [134, 146, 238, 248, 145, 139, 236] {
  n = 100*a + 10*b + c with 0 < a < b < c < 10
  } 3 digit numbers whose digits are in strictly ascending order
  
• [176, 298, 295, 251, 330, 258, and 211] {
  n = 100*a + 10*b + c, b is odd
  } 3 digit numbers where the middle digit is odd
  
• [20, 56, 60, 85, 36, 41, 66, 79, 82] {
  9 < n < 100
  2 digit numbers
  
• [361, 283, 343, 223, 241, 355, 331, 91] {
  n ≡ 1 (mod 6)
  } (multiples of 6) + 1
  
• [105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
  
• [244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
  
• [347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
  
• [65, 345 285, 240, 160, 70, 225] {
  5 | n
  } multiples of 5
  
• [47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
  
• [80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
  
• [102, 366, 87, 108, 198, 264, 159] {
  3 | n
  } multiplies of 3
  
• [73, 157, 231, 35, 111, 72, 101] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
  } Numbers none of whose digits are composite
  
• [318, 266, 208, 154, 64, 6, 350] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
  } Even numbers whose digit sum is also even

Topology: Micc, Not_Mafia: 89 points

• [171, 323, 77] palindromes
  
• [249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

• [46, 59, 164] {
  n ≡ ±1 (mod 15)
  } numbers equivalent to ±1 mod 15
  
• [286, 207, 349] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
  } Numbers whose digit sum is a perfect square
  
• [23, 293, 161] {
  n ≡ 5 (mod 6)
  } numbers equivalent to 5 mod 6
  
• [69. 99, 269] numbers that contain a 9

Dynamics: lilith2013, skitter30: 99 points

• [328, 28, 276, 275] numbers that contain a 27 or 28
  
• [124, 214, 282] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers that consist only of digits that are powers of 2 (including 1)
  
• [81, 189, 324, 27, 297] {
  27 | n
  } multiples of 27
  
• [360, 152, 265] {
  n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
  } second digit from the right is strictly the largest digit

It is

Not_Mafia

's turn.

There are 19 cards remaining

It looks fine to me. Are ties okay, like 332? Or should it be strictly larger than the other digits?

[lilith2013]

I was thinking strictly larger?

[Plotinus]

Thanks for clarifying it

[Not_Mafia]

277, 51, 165

Odd numbers that also contain an odd digit that isn’t the last digit

[vincentw]

Add 294 to the 9s sequence.

[Plotinus]

Spoiler: completed sequences

• [54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
  
• [78, 126, 336, 348, 192, 315, 123] {
  n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
  } composite numbers whose digit sum is composite
  
• [55, 226, 253, 190, 19, 352, 334] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
  } numbers whose digit sum equals 10
  
• [3, 7, 229, 5, 179, 17, 137] primes
  
• [25, 44, 63, 365, 52, 62, 88, 175] {
  i % (i % 10) == 0
  } Numbers divisible by their last digit
  
• [166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
  
• [1, 4, 43, 141, 301, 302, 341] have four or fewer factors
  
• [90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
  
• [234, 342, 356, 140, 173, 200, 280, 299] {
  n = 100×a + 10×b + c with c < a + b
  } 3 digit numbers where the last digit is less than the sum of the first two digits
  
• [39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
  
• [174, 118, 274, 232, 316, 180, 358 ] {
  2 | n ∧ n ≥ 100
  } 3 digit even numbers
  
• [48, 135, 306, 40, 84, 132, 243] {
  k² | n, k > 1
  } numbers that are divisible by a perfect square greater than one
  
• [235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
  
• [125, 270, 320, 30, 45, 100, 150] {
  2ⁱ×3^j×5^k with i, j, k ≥ 0
  } 5-smooth numbers
  
• [202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
  
• [120, 143, 194, 8, 15, 98, 170] {
  n ∈ [k² - 2, k² + 2], k ∈ ℤ
  numbers within 2 of a perfect square
  
• [191, 359, 305, 271, 199, 163, 109] {
  n > 100 ∧ n % 2 = 1
  } 3 digit odd numbers
  
• [128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
  
• [116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
  
• [16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
  
• [95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
  
• [37, 53, 75, 339, 9, 57, 197] all digits are odd
  
• [220, 162, 18, 42, 107, 201, 213, 230]
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers where the sum of the digits is a single digit
  
• [121, 209, 252, 29, 67, 92, 119 ] {
  (n(n+1)/2 + 1) or (n(n+1)/2 - 1)
  } numbers that are exactly one away from a triangular number
  
• [134, 146, 238, 248, 145, 139, 236] {
  n = 100*a + 10*b + c with 0 < a < b < c < 10
  } 3 digit numbers whose digits are in strictly ascending order
  
• [176, 298, 295, 251, 330, 258, and 211] {
  n = 100*a + 10*b + c, b is odd
  } 3 digit numbers where the middle digit is odd
  
• [20, 56, 60, 85, 36, 41, 66, 79, 82] {
  9 < n < 100
  2 digit numbers
  
• [361, 283, 343, 223, 241, 355, 331, 91] {
  n ≡ 1 (mod 6)
  } (multiples of 6) + 1
  
• [105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
  
• [244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
  
• [347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
  
• [65, 345 285, 240, 160, 70, 225] {
  5 | n
  } multiples of 5
  
• [47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
  
• [80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
  
• [102, 366, 87, 108, 198, 264, 159] {
  3 | n
  } multiplies of 3
  
• [73, 157, 231, 35, 111, 72, 101] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
  } Numbers none of whose digits are composite
  
• [318, 266, 208, 154, 64, 6, 350] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
  } Even numbers whose digit sum is also even

Topology: Micc, Not_Mafia: 89 points

• [171, 323, 77] palindromes
  
• [249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.
  
• [277, 51, 165] {
  n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
  } Odd numbers that also contain an odd digit that isn’t the last digit

Measure: StrangerCoug, vincentw: 84 points

• [46, 59, 164] {
  n ≡ ±1 (mod 15)
  } numbers equivalent to ±1 mod 15
  
• [286, 207, 349] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
  } Numbers whose digit sum is a perfect square
  
• [23, 293, 161] {
  n ≡ 5 (mod 6)
  } numbers equivalent to 5 mod 6
  
• [69, 99, 269, 294] numbers that contain a 9

Dynamics: lilith2013, skitter30: 99 points

• [328, 28, 276, 275] numbers that contain a 27 or 28
  
• [124, 214, 282] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers that consist only of digits that are powers of 2 (including 1)
  
• [81, 189, 324, 27, 297] {
  27 | n
  } multiples of 27
  
• [360, 152, 265] {
  n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
  } second digit from the right is strictly the largest digit

It is

skitter30

's turn.

There are 15 cards remaining

[StrangerCoug]

Redacted; see following post.

[Micc]

I think you’ve played out of turn SC

[StrangerCoug]

Oops Will replay it on my turn since you've seen what it was.

[skitter30]

49, 94, 148
numbers whose digits sum to 13

[Plotinus]

Spoiler: completed sequences

• [54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
  
• [78, 126, 336, 348, 192, 315, 123] {
  n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
  } composite numbers whose digit sum is composite
  
• [55, 226, 253, 190, 19, 352, 334] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
  } numbers whose digit sum equals 10
  
• [3, 7, 229, 5, 179, 17, 137] primes
  
• [25, 44, 63, 365, 52, 62, 88, 175] {
  i % (i % 10) == 0
  } Numbers divisible by their last digit
  
• [166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
  
• [1, 4, 43, 141, 301, 302, 341] have four or fewer factors
  
• [90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
  
• [234, 342, 356, 140, 173, 200, 280, 299] {
  n = 100×a + 10×b + c with c < a + b
  } 3 digit numbers where the last digit is less than the sum of the first two digits
  
• [39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
  
• [174, 118, 274, 232, 316, 180, 358 ] {
  2 | n ∧ n ≥ 100
  } 3 digit even numbers
  
• [48, 135, 306, 40, 84, 132, 243] {
  k² | n, k > 1
  } numbers that are divisible by a perfect square greater than one
  
• [235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
  
• [125, 270, 320, 30, 45, 100, 150] {
  2ⁱ×3^j×5^k with i, j, k ≥ 0
  } 5-smooth numbers
  
• [202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
  
• [120, 143, 194, 8, 15, 98, 170] {
  n ∈ [k² - 2, k² + 2], k ∈ ℤ
  numbers within 2 of a perfect square
  
• [191, 359, 305, 271, 199, 163, 109] {
  n > 100 ∧ n % 2 = 1
  } 3 digit odd numbers
  
• [128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
  
• [116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
  
• [16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
  
• [95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
  
• [37, 53, 75, 339, 9, 57, 197] all digits are odd
  
• [220, 162, 18, 42, 107, 201, 213, 230]
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers where the sum of the digits is a single digit
  
• [121, 209, 252, 29, 67, 92, 119 ] {
  (n(n+1)/2 + 1) or (n(n+1)/2 - 1)
  } numbers that are exactly one away from a triangular number
  
• [134, 146, 238, 248, 145, 139, 236] {
  n = 100*a + 10*b + c with 0 < a < b < c < 10
  } 3 digit numbers whose digits are in strictly ascending order
  
• [176, 298, 295, 251, 330, 258, and 211] {
  n = 100*a + 10*b + c, b is odd
  } 3 digit numbers where the middle digit is odd
  
• [20, 56, 60, 85, 36, 41, 66, 79, 82] {
  9 < n < 100
  2 digit numbers
  
• [361, 283, 343, 223, 241, 355, 331, 91] {
  n ≡ 1 (mod 6)
  } (multiples of 6) + 1
  
• [105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
  
• [244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
  
• [347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
  
• [65, 345 285, 240, 160, 70, 225] {
  5 | n
  } multiples of 5
  
• [47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
  
• [80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
  
• [102, 366, 87, 108, 198, 264, 159] {
  3 | n
  } multiplies of 3
  
• [73, 157, 231, 35, 111, 72, 101] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
  } Numbers none of whose digits are composite
  
• [318, 266, 208, 154, 64, 6, 350] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
  } Even numbers whose digit sum is also even

Topology: Micc, Not_Mafia: 89 points

• [171, 323, 77] palindromes
  
• [249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.
  
• [277, 51, 165] {
  n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
  } Odd numbers that also contain an odd digit that isn’t the last digit

Measure: StrangerCoug, vincentw: 84 points

• [46, 59, 164] {
  n ≡ ±1 (mod 15)
  } numbers equivalent to ±1 mod 15
  
• [286, 207, 349] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
  } Numbers whose digit sum is a perfect square
  
• [23, 293, 161] {
  n ≡ 5 (mod 6)
  } numbers equivalent to 5 mod 6
  
• [69, 99, 269, 294] numbers that contain a 9

Dynamics: lilith2013, skitter30: 99 points

• [328, 28, 276, 275] numbers that contain a 27 or 28
  
• [124, 214, 282] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers that consist only of digits that are powers of 2 (including 1)
  
• [81, 189, 324, 27, 297] {
  27 | n
  } multiples of 27
  
• [360, 152, 265] {
  n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
  } second digit from the right is strictly the largest digit
  
• [49, 94, 148] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
  } digits sum to 13

It is

Micc

's turn.

There are 12 cards remaining

[Micc]

181, 13, 327, 291, and 169 to complete odd numbers with an odd digit that isn’t the last one.

[Plotinus]

StrangerCoug has submitted his turn by PM:

Reinstate my out-of-turn play of adding 14 to the numbers whose digits are powers of two when it's my turn, please.

Spoiler: completed sequences

• [54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
  
• [78, 126, 336, 348, 192, 315, 123] {
  n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
  } composite numbers whose digit sum is composite
  
• [55, 226, 253, 190, 19, 352, 334] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
  } numbers whose digit sum equals 10
  
• [3, 7, 229, 5, 179, 17, 137] primes
  
• [25, 44, 63, 365, 52, 62, 88, 175] {
  i % (i % 10) == 0
  } Numbers divisible by their last digit
  
• [166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
  
• [1, 4, 43, 141, 301, 302, 341] have four or fewer factors
  
• [90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
  
• [234, 342, 356, 140, 173, 200, 280, 299] {
  n = 100×a + 10×b + c with c < a + b
  } 3 digit numbers where the last digit is less than the sum of the first two digits
  
• [39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
  
• [174, 118, 274, 232, 316, 180, 358 ] {
  2 | n ∧ n ≥ 100
  } 3 digit even numbers
  
• [48, 135, 306, 40, 84, 132, 243] {
  k² | n, k > 1
  } numbers that are divisible by a perfect square greater than one
  
• [235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
  
• [125, 270, 320, 30, 45, 100, 150] {
  2ⁱ×3^j×5^k with i, j, k ≥ 0
  } 5-smooth numbers
  
• [202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
  
• [120, 143, 194, 8, 15, 98, 170] {
  n ∈ [k² - 2, k² + 2], k ∈ ℤ
  numbers within 2 of a perfect square
  
• [191, 359, 305, 271, 199, 163, 109] {
  n > 100 ∧ n % 2 = 1
  } 3 digit odd numbers
  
• [128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
  
• [116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
  
• [16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
  
• [95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
  
• [37, 53, 75, 339, 9, 57, 197] all digits are odd
  
• [220, 162, 18, 42, 107, 201, 213, 230]
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers where the sum of the digits is a single digit
  
• [121, 209, 252, 29, 67, 92, 119 ] {
  (n(n+1)/2 + 1) or (n(n+1)/2 - 1)
  } numbers that are exactly one away from a triangular number
  
• [134, 146, 238, 248, 145, 139, 236] {
  n = 100*a + 10*b + c with 0 < a < b < c < 10
  } 3 digit numbers whose digits are in strictly ascending order
  
• [176, 298, 295, 251, 330, 258, and 211] {
  n = 100*a + 10*b + c, b is odd
  } 3 digit numbers where the middle digit is odd
  
• [20, 56, 60, 85, 36, 41, 66, 79, 82] {
  9 < n < 100
  2 digit numbers
  
• [361, 283, 343, 223, 241, 355, 331, 91] {
  n ≡ 1 (mod 6)
  } (multiples of 6) + 1
  
• [105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
  
• [244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
  
• [347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
  
• [65, 345 285, 240, 160, 70, 225] {
  5 | n
  } multiples of 5
  
• [47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
  
• [80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
  
• [102, 366, 87, 108, 198, 264, 159] {
  3 | n
  } multiplies of 3
  
• [73, 157, 231, 35, 111, 72, 101] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
  } Numbers none of whose digits are composite
  
• [318, 266, 208, 154, 64, 6, 350] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
  } Even numbers whose digit sum is also even
  
• [277, 51, 165, 181, 13, 327, 291, and 169] {
  n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
  } Odd numbers that also contain an odd digit that isn’t the last digit

Topology: Micc, Not_Mafia: 97 points

• [171, 323, 77] palindromes
  
• [249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

• [46, 59, 164] {
  n ≡ ±1 (mod 15)
  } numbers equivalent to ±1 mod 15
  
• [286, 207, 349] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
  } Numbers whose digit sum is a perfect square
  
• [23, 293, 161] {
  n ≡ 5 (mod 6)
  } numbers equivalent to 5 mod 6
  
• [69, 99, 269, 294] numbers that contain a 9
  
• [124, 214, 282, 14] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers that consist only of digits that are powers of 2 (including 1)

Dynamics: lilith2013, skitter30: 99 points

• [328, 28, 276, 275] numbers that contain a 27 or 28
  
• [81, 189, 324, 27, 297] {
  27 | n
  } multiples of 27
  
• [360, 152, 265] {
  n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
  } second digit from the right is strictly the largest digit
  
• [49, 94, 148] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
  } digits sum to 13

It is

lilith2013

's turn.

There are 6 cards remaining

[lilith2013]

Add 262 to second to last digit is the largest

[Plotinus]

Spoiler: completed sequences

• [54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
  
• [78, 126, 336, 348, 192, 315, 123] {
  n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
  } composite numbers whose digit sum is composite
  
• [55, 226, 253, 190, 19, 352, 334] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
  } numbers whose digit sum equals 10
  
• [3, 7, 229, 5, 179, 17, 137] primes
  
• [25, 44, 63, 365, 52, 62, 88, 175] {
  i % (i % 10) == 0
  } Numbers divisible by their last digit
  
• [166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
  
• [1, 4, 43, 141, 301, 302, 341] have four or fewer factors
  
• [90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
  
• [234, 342, 356, 140, 173, 200, 280, 299] {
  n = 100×a + 10×b + c with c < a + b
  } 3 digit numbers where the last digit is less than the sum of the first two digits
  
• [39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
  
• [174, 118, 274, 232, 316, 180, 358 ] {
  2 | n ∧ n ≥ 100
  } 3 digit even numbers
  
• [48, 135, 306, 40, 84, 132, 243] {
  k² | n, k > 1
  } numbers that are divisible by a perfect square greater than one
  
• [235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
  
• [125, 270, 320, 30, 45, 100, 150] {
  2ⁱ×3^j×5^k with i, j, k ≥ 0
  } 5-smooth numbers
  
• [202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
  
• [120, 143, 194, 8, 15, 98, 170] {
  n ∈ [k² - 2, k² + 2], k ∈ ℤ
  numbers within 2 of a perfect square
  
• [191, 359, 305, 271, 199, 163, 109] {
  n > 100 ∧ n % 2 = 1
  } 3 digit odd numbers
  
• [128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
  
• [116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
  
• [16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
  
• [95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
  
• [37, 53, 75, 339, 9, 57, 197] all digits are odd
  
• [220, 162, 18, 42, 107, 201, 213, 230]
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers where the sum of the digits is a single digit
  
• [121, 209, 252, 29, 67, 92, 119 ] {
  (n(n+1)/2 + 1) or (n(n+1)/2 - 1)
  } numbers that are exactly one away from a triangular number
  
• [134, 146, 238, 248, 145, 139, 236] {
  n = 100*a + 10*b + c with 0 < a < b < c < 10
  } 3 digit numbers whose digits are in strictly ascending order
  
• [176, 298, 295, 251, 330, 258, and 211] {
  n = 100*a + 10*b + c, b is odd
  } 3 digit numbers where the middle digit is odd
  
• [20, 56, 60, 85, 36, 41, 66, 79, 82] {
  9 < n < 100
  2 digit numbers
  
• [361, 283, 343, 223, 241, 355, 331, 91] {
  n ≡ 1 (mod 6)
  } (multiples of 6) + 1
  
• [105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
  
• [244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
  
• [347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
  
• [65, 345 285, 240, 160, 70, 225] {
  5 | n
  } multiples of 5
  
• [47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
  
• [80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
  
• [102, 366, 87, 108, 198, 264, 159] {
  3 | n
  } multiplies of 3
  
• [73, 157, 231, 35, 111, 72, 101] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
  } Numbers none of whose digits are composite
  
• [318, 266, 208, 154, 64, 6, 350] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
  } Even numbers whose digit sum is also even
  
• [277, 51, 165, 181, 13, 327, 291, and 169] {
  n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
  } Odd numbers that also contain an odd digit that isn’t the last digit

Topology: Micc, Not_Mafia: 97 points

• [171, 323, 77] palindromes
  
• [249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

• [46, 59, 164] {
  n ≡ ±1 (mod 15)
  } numbers equivalent to ±1 mod 15
  
• [286, 207, 349] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
  } Numbers whose digit sum is a perfect square
  
• [23, 293, 161] {
  n ≡ 5 (mod 6)
  } numbers equivalent to 5 mod 6
  
• [69, 99, 269, 294] numbers that contain a 9
  
• [124, 214, 282, 14] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers that consist only of digits that are powers of 2 (including 1)

Dynamics: lilith2013, skitter30: 99 points

• [328, 28, 276, 275] numbers that contain a 27 or 28
  
• [81, 189, 324, 27, 297] {
  27 | n
  } multiples of 27
  
• [360, 152, 265, 262] {
  n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
  } second digit from the right is strictly the largest digit
  
• [49, 94, 148] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
  } digits sum to 13

It is

Not_Mafia

's turn.

There are 5 cards remaining

[lilith2013]

I broke my streak of only completing or starting sequences </3

[Not_Mafia]

24, 12, 21, to complete numbers that consist only of digits that are powers of 2 (including 1)

Finally, I've been one number off of this and a couple of others for several turns now

[Micc]

Nice play! puts us in the lead, but its still real close

[Plotinus]

Spoiler: completed sequences

• [54, 183, 272, 313, 115, 182, 278, 218 ] Numbers where you can ignore 1 digit and use mathematical operators on the remaining digits to get 4
  
• [78, 126, 336, 348, 192, 315, 123] {
  n is composite and n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i is composite; a_i ≥ 0, d > 0
  } composite numbers whose digit sum is composite
  
• [55, 226, 253, 190, 19, 352, 334] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 10; a_i ≥ 0, d > 0
  } numbers whose digit sum equals 10
  
• [3, 7, 229, 5, 179, 17, 137] primes
  
• [25, 44, 63, 365, 52, 62, 88, 175] {
  i % (i % 10) == 0
  } Numbers divisible by their last digit
  
• [166, 337, 333, 112, 311, 155, 144, 338] Numbers with at least one immediately repeating digit
  
• [1, 4, 43, 141, 301, 302, 341] have four or fewer factors
  
• [90, 322, 303, 329, 136, 210, 149, 228, 38, 188] numbers that are composite after removing the smallest digit
  
• [234, 342, 356, 140, 173, 200, 280, 299] {
  n = 100×a + 10×b + c with c < a + b
  } 3 digit numbers where the last digit is less than the sum of the first two digits
  
• [39, 86, 261, 32, 33, 76, 93] can be spelled digit by digit with ten or fewer letters in English, no leading zeroes, 0 is spelled as zero
  
• [174, 118, 274, 232, 316, 180, 358 ] {
  2 | n ∧ n ≥ 100
  } 3 digit even numbers
  
• [48, 135, 306, 40, 84, 132, 243] {
  k² | n, k > 1
  } numbers that are divisible by a perfect square greater than one
  
• [235, 242, 268, 259, 22, 34, 195, 97] numbers with a 2-digit prime factor
  
• [125, 270, 320, 30, 45, 100, 150] {
  2ⁱ×3^j×5^k with i, j, k ≥ 0
  } 5-smooth numbers
  
• [202, 351, 204, 260, 296, 300, 354] have a three digit factor other than itself
  
• [120, 143, 194, 8, 15, 98, 170] {
  n ∈ [k² - 2, k² + 2], k ∈ ℤ
  numbers within 2 of a perfect square
  
• [191, 359, 305, 271, 199, 163, 109] {
  n > 100 ∧ n % 2 = 1
  } 3 digit odd numbers
  
• [128, 196, 319, 193, 172, 158, 288] numbers wherein if i spell the numbers out digit by digit in english, i can take the first letter of each digit and use those letters to form an english word (i.e. anagrams are allowed)
  
• [116, 217, 219, 215, 114, 127, 222] Three digit numbers in which you can draw a date separator between two digits and get a valid date in both month/day and day/month format (not necessarily with the separator in the same place)—the separator must follow, not precede, a medial zero
  
• [16, 113, 153, 281, 325, 353, 364] any side of all primitive Pythagorean triangles with its hypotenuse no larger than the largest number in the deck
  
• [95, 138, 246, 58, 335, 314, 247] squarefree composite numbers
  
• [37, 53, 75, 339, 9, 57, 197] all digits are odd
  
• [220, 162, 18, 42, 107, 201, 213, 230]
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 0 < Σ_i∈[0,d]a_i < 10; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers where the sum of the digits is a single digit
  
• [121, 209, 252, 29, 67, 92, 119 ] {
  (n(n+1)/2 + 1) or (n(n+1)/2 - 1)
  } numbers that are exactly one away from a triangular number
  
• [134, 146, 238, 248, 145, 139, 236] {
  n = 100*a + 10*b + c with 0 < a < b < c < 10
  } 3 digit numbers whose digits are in strictly ascending order
  
• [176, 298, 295, 251, 330, 258, and 211] {
  n = 100*a + 10*b + c, b is odd
  } 3 digit numbers where the middle digit is odd
  
• [20, 56, 60, 85, 36, 41, 66, 79, 82] {
  9 < n < 100
  2 digit numbers
  
• [361, 283, 343, 223, 241, 355, 331, 91] {
  n ≡ 1 (mod 6)
  } (multiples of 6) + 1
  
• [105, 122, 239, 287, 50, 177, 263] digit sum is squarefree (1 counts as squarefree)
  
• [244, 267, 212, 221, 288, 227, 206] numbers where the amount of digits that are "2" is an infinitely recurring percentage
  
• [347, 130, 357, 233, 133, 307, 340, 362] numbers where the amount of digits that are "3" is an infinitely recurring percentage.
  
• [65, 345 285, 240, 160, 70, 225] {
  5 | n
  } multiples of 5
  
• [47, 74, 131, 245, 71, 117, 151] remove each digit that is a power of 2 (including 1) and you're left with a prime
  
• [80, 187, 345, 156, 178, 185 344] numbers that contain an L when written in roman numerals
  
• [102, 366, 87, 108, 198, 264, 159] {
  3 | n
  } multiplies of 3
  
• [73, 157, 231, 35, 111, 72, 101] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_ii is not composite, d > 0 ∈ ℤ
  } Numbers none of whose digits are composite
  
• [318, 266, 208, 154, 64, 6, 350] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 2 | Σ_i∈[0,d]a_i and 2 | n, d > 0 ∈ ℤ
  } Even numbers whose digit sum is also even
  
• [277, 51, 165, 181, 13, 327, 291, and 169] {
  n = 100×a + 10×b + c with c is odd and (a is odd or b is odd) and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
  } Odd numbers that also contain an odd digit that isn’t the last digit
  
• [124, 214, 282, 14, 24, 12, 21] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i = 2^k; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers that consist only of digits that are powers of 2 (including 1)

Topology: Micc, Not_Mafia: 104 points

• [171, 323, 77] palindromes
  
• [249, 224, 292] Remove each digit that is a 2 and you are left with a perfect square.

Measure: StrangerCoug, vincentw: 84 points

• [46, 59, 164] {
  n ≡ ±1 (mod 15)
  } numbers equivalent to ±1 mod 15
  
• [286, 207, 349] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = k²; a_i ≥ 0, d > 0; k ∈ ℤ
  } Numbers whose digit sum is a perfect square
  
• [23, 293, 161] {
  n ≡ 5 (mod 6)
  } numbers equivalent to 5 mod 6
  
• [69, 99, 269, 294] numbers that contain a 9

Dynamics: lilith2013, skitter30: 99 points

• [328, 28, 276, 275] numbers that contain a 27 or 28
  
• [81, 189, 324, 27, 297] {
  27 | n
  } multiples of 27
  
• [360, 152, 265, 262] {
  n = 100×a + 10×b + c with b > a, c, and 0 ≤ a, b, c ≤ 9, {a, b, c} ∈ ℤ
  } second digit from the right is strictly the largest digit
  
• [49, 94, 148] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with Σ_i∈[0,d]a_i = 13; a_i ≥ 0, d > 0
  } digits sum to 13

It is

vincentw

's turn.

There are 2 cards remaining. When we run out of cards we'll keep playing until

4

6

people pass in a row. You can pass only if there are no sequences to which you can add a card.

[vincentw]

This late in the game, a bingo might not be the smartest move, but my hand can't complete any one sequence and I don't wanna risk playing one number and drawing a number that doesn't fit this sequence, so this will have to do.

Play my whole hand as "Day numbers that fall in the first 2 weeks of its respective month". A day number is such that 1 corresponds to 1st Jan, 2 to 2nd Jan and so on until 366 meaning 31st Dec. Because the deck reaches 366, it's only natural for the day number to include a leap day; however, my hand also works with day numbers for non-leap years, if it matters.
My hand translates to 2nd Jan, 10th Jan, 3rd Aug, 11th Sep, 5th Oct, 3rd Nov, and 5th Nov.

There are 168 qualifying numbers, which is less than half the deck. The only meta rule that I can think of is if I switch out "first" for "last", and it has 168 different numbers. Doing 2×(168 choose 7)/(366 choose 7) comes up to be around .8%.

(Shouldn't it be 6 because we have 6 players?)