Sequencer | StrangerCoug's turn

[Plotinus]

Deathrowkitty has been prodded. It will be Felisan's turn in (expired on 2019-10-16 08:18:00) or as soon as DeathRowKitty posts, whichever happens first.

[DeathRowKitty]

[12, 62, 85]

numbers that are the sum of the proper divisors of some number < 1000 not in the deck for this game.

12 is the sum of the proper divisors of 121 (1 and 11)
62 is the sum of the proper divisors of 118 (1, 2, and 59)
85 is the sum of the proper divisors of 923 (1, 13, and 71)

[Felissan]

I complete the sequence DRK has just created using 20, 35, 95 and 100.

20 is the sum of the proper divisors of 361 (1 and 19)
35 is the sum of the proper divisors of 145 (1, 5 and 29)
95 is the sum of the proper divisors of 445 (1, 5 and 89)
100 is the sum of the proper divisors of 194 (1, 2 and 97)

I've just spent the last half-hour or something looking for a way to fit that one big-ass number in my hand, but sadly the <1000 limit prevented me from earning the truckload of style points that would have come along with one extra in-game point.

[DeathRowKitty]

Ha, nice

that's what I get for being lazy about my sequence choices

[Plotinus]

Spoiler: Finished sequences:

• {
  n² ± [0, 2]
  } numbers within 2 of a perfect square,
  
• {
  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
  
• {
  n is 0 or odd (mod 9)
  } numbers that are odd when you repeatedly sum their digits
  
• n is the sum of the Scrabble point values of the letters in the US spelling of the numbers in the deck.
  
• numbers that are the sum of the proper divisors of some number < 1000 not in the deck for this game.

McMenno has:

• [14, 35, 343] {
  7n
  } divisible by 7
  
• [5, 6, 100] numbers used in 0, including substrings of other numbers, but not including the deck spoiler
  
• [56, 57, 64, 76] 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)

Implosion has 14 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)

DeathRowKitty has 9 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 7 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
  
• [79, 87, 92] {
  maxdigit(n) > 7
  } numbers that contain an 8 or 9

NotMySpamAccount has:

• [4, 20, 36, 68] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [4, 16, 25, 81] {
  n²
  } squares

StrangerCoug has 7 points and:

• [11, 17, 19, 71, 43] primes
  
• [1, 10, 15] {
  n*(n-1)/2)
  }: triangular numbers

There are 105 cards left in the deck. It is NotMySpamAccount's turn

[Plotinus]

NotMySpamAccount has been prodded. It will be StrangerCoug's turn in (expired on 2019-10-17 13:42:04) or as soon as NotMySpamAccount goes, whichever happens first.

[NotMySpamAccount]

My bad, sorry.

29 and 83 to the primes, finishing it.

[StrangerCoug]

Add 28 to the triangulars

[Plotinus]

Spoiler: Finished sequences:

• {
  n² ± [0, 2]
  } numbers within 2 of a perfect square,
  
• {
  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
  
• {
  n is 0 or odd (mod 9)
  } numbers that are odd when you repeatedly sum their digits
  
• n is the sum of the Scrabble point values of the letters in the US spelling of the numbers in the deck.
  
• numbers that are the sum of the proper divisors of some number < 1000 not in the deck for this game.
  
• primes

McMenno has:

• [14, 35, 343] {
  7n
  } divisible by 7
  
• [5, 6, 100] numbers used in 0, including substrings of other numbers, but not including the deck spoiler
  
• [56, 57, 64, 76] 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)

Implosion has 14 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)

DeathRowKitty has 9 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 7 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
  
• [79, 87, 92] {
  maxdigit(n) > 7
  } numbers that contain an 8 or 9

popsofctown has 7 points and:

• [4, 20, 36, 68] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [4, 16, 25, 81] {
  n²
  } squares

StrangerCoug has 7 points and:

• [1, 10, 15, 28] {
  n*(n-1)/2)
  }: triangular numbers

There are 102 cards left in the deck. It is McMenno's turn

[Plotinus]

NotMySpamAccount has requested replacement. If it is their turn before a replacement is found, they will be skipped.

[Plotinus]

popsofctown replaces NotMySpamAccount! Yay!

[Plotinus]

McMenno has been prodded. It will be implosion's turn in (expired on 2019-10-19 01:42:06) or as soon as McMenno goes, whichever happens first.

[Plotinus]

implosion has been prodded. It will be DeathRowKity's turn in (expired on 2019-10-21 07:56:00) or as soon as implosion goes, whichever happens first.

[StrangerCoug]

Dang, where is everyone?

[DeathRowKitty]

We were trying to set up the sequence of post numbers of 7 consecutive posts in this thread all made by Plotinus

[implosion]

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).

5 -> 9 -> 13
6 -> 9 -> 13
50 -> 55 -> 64
125 -> 145 -> 164

[Plotinus]

Spoiler: Finished sequences:

• {
  n² ± [0, 2]
  } numbers within 2 of a perfect square,
  
• {
  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
  
• {
  n is 0 or odd (mod 9)
  } numbers that are odd when you repeatedly sum their digits
  
• n is the sum of the Scrabble point values of the letters in the US spelling of the numbers in the deck.
  
• numbers that are the sum of the proper divisors of some number < 1000 not in the deck for this game.
  
• primes

McMenno has:

• [14, 35, 343] {
  7n
  } divisible by 7
  
• [5, 6, 100] numbers used in 0, including substrings of other numbers, but not including the deck spoiler
  
• [56, 57, 64, 76] 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)

Implosion has 14 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 9 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 7 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
  
• [79, 87, 92] {
  maxdigit(n) > 7
  } numbers that contain an 8 or 9

popsofctown has 7 points and:

• [4, 20, 36, 68] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [4, 16, 25, 81] {
  n²
  } squares

StrangerCoug has 7 points and:

• [1, 10, 15, 28] {
  n*(n-1)/2)
  }: triangular numbers

There are 98 cards left in the deck. It is DeathRowKitty's turn

[DeathRowKitty]

Add [13, 15, 16, 27] to numbers in the opening post

[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

McMenno has:

• [14, 35, 343] {
  7n
  } divisible by 7
  
• [56, 57, 64, 76] 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)

Implosion has 14 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 16 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 7 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
  
• [79, 87, 92] {
  maxdigit(n) > 7
  } numbers that contain an 8 or 9

popsofctown has 7 points and:

• [4, 20, 36, 68] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [4, 16, 25, 81] {
  n²
  } squares

StrangerCoug has 7 points and:

• [1, 10, 15, 28] {
  n*(n-1)/2)
  }: triangular numbers

There are 94 cards left in the deck. It is Felissan's turn

edit: I've added the numbers back into the completed sequences spoiler. I was removing them from completed sequences because they took up too much room on discord and made it hard to tell which sequences can still be added to, but this problem doesn't exist on the forum and it's nice to have them there.

[Felissan]

I complete the Cantor set sequence with 10, 21 and 729.

(7/27-8/27) is removed in step 3; (1/3-2/3) is removed in step 1, and 1/3 = 9/27.
(19/27-20/27) is removed in step 3.
(727/729-728/729) is removed in step 6.

[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)

McMenno has:

• [14, 35, 343] {
  7n
  } divisible by 7

Implosion has 14 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 16 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 14 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
  
• [79, 87, 92] {
  maxdigit(n) > 7
  } numbers that contain an 8 or 9

popsofctown has 7 points and:

• [4, 20, 36, 68] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [4, 16, 25, 81] {
  n²
  } squares

StrangerCoug has 7 points and:

• [1, 10, 15, 28] {
  n*(n-1)/2)
  }: triangular numbers

There are 91 cards left in the deck. It is popsofctown's turn

[popsofctown]

I AM HERE

[popsofctown]

I spent over 2 hours on Wikipedia trying to figure out how to determine the valid numbers for DRK's sequence and I don't think I can do it unless I buy a pack of 52 playing cards and painstakingly use pen and paper

[popsofctown]

Also all of implosion's sequences are sadism

[popsofctown]

Composites for which you can take the greatest factor that is less than the composite, then subtract any positive preferred factor of the composite, and receive as the result a perfect number

55, 58, 60.