Sequencer | StrangerCoug's turn

[Plotinus]

McMenno has:

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

Implosion has:

• [15, 53, 91] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i ≡ 1 (mod 2) ∀ i ∈ [1, 9], ∀ d > 1
  } numbers with at least two digits, all of which are odd

DeathRowKitty has:

• [8, 18, 34] n is the sum of the Scrabble point values of the letters in the US spelling of the numbers in the deck.

Felissan has:

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

NotMySpamAccount has:

• [2, 4, 32] {
  2ⁿ
  } powers of two

StrangerCoug has:

• [17, 19, 43] primes

It is McMenno's turn

[StrangerCoug]

Mod: You misspelled my username (there should be only two R's).

[McMenno]

Number used in the opening post, except in the "deck" tab

5, 6, 100

[Plotinus]

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

Implosion has:

• [15, 53, 91] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with a_i ≡ 1 (mod 2) ∀ i ∈ [1, 9], ∀ d > 1
  } numbers with at least two digits, all of which are odd

DeathRowKitty has:

• [8, 18, 34] n is the sum of the Scrabble point values of the letters in the US spelling of the numbers in the deck.

Felissan has:

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

NotMySpamAccount has:

• [2, 4, 32] {
  2ⁿ
  } powers of two

StrangerCoug has:

• [17, 19, 43] primes

It is implosion's turn

[McMenno]

no substrings

[Plotinus]

where's the 6 in the OP?

[implosion]

In the mean time I'll just make my move, since it's unaffected by menno's and to keep the game moving:

[5, 9, 10, 27, 48, 66, 98] {

n² + k, -3 < k < 3

} numbers that are within two of a perfect square
(4, 9, 9, 25, 49, 64, 100 are the close squares)

Note that each of the 10 squares 1² through 10² contributes at most 5 numbers to this set between 1 and 100, and there is some overlap, so it contains fewer than 50 of the numbers between 1 and 100.

[StrangerCoug]

Good bingo

[McMenno]

substrings have been deemed fine by the council of mcmennos

[Plotinus]

Great. I don't want to do too much reinterpreting of sequences, and the original player has the final say on what the rules for the sequence are. Please speak up if I misinterpret your rules. I think it is okay to work together to make the starting move a sequence be valid or make the closed form be error free.

It would have been better if I pointed out the problem with the six initially and offered to let McMenno come up with a change himself. I'll try to do that in the future, because I think I did overstep here. Sorry about that.

Finished:

{

n² ± [0, 2]

} numbers within 2 of a perfect square

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

Implosion has 7 points and:

• [15, 53, 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

DeathRowKitty has:

• [8, 18, 34] n is the sum of the Scrabble point values of the letters in the US spelling of the numbers in the deck.

Felissan has:

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

NotMySpamAccount has:

• [2, 4, 32] {
  2ⁿ
  } powers of two

StrangerCoug has:

• [17, 19, 43] primes

It is DeathRowKitty's turn

[DeathRowKitty]

[38, 82, 84]

Consider a standard 52 card deck that starts in Ace - King, Ace - King, Ace - King, Ace - King order. Number the cards 1-52 in order with the first ace as 1 and the final king as 52. Suppose you perform an infinite sequence of perfect out-shuffles on this deck, each time renumbering the cards in the deck according to their new order. My sequence is those numbers that do not differ by a multiple of 52 from any number that ever indexes a non-face card (face cards are jack, queen, and king) that is 1 greater than a multiple of 4. So basically no ace, 5, or 9 can ever be numbered with a number in the sequence or any number ≡ mod 52 to any number in the sequence.

Every card ever numbered 38 is a 3, 6, 8, 10, J, or Q
Every card ever numbered 32 (84) is also a 3, 6, 8, 10, J, or Q
Every card ever numbered 30 (82) is a 2, 3, 4, 6, 8, or J

[Plotinus]

Finished:

{

n² ± [0, 2]

} numbers within 2 of a perfect square

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

Implosion has 7 points and:

• [15, 53, 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

DeathRowKitty has:

• [8, 18, 34] n is the sum of the Scrabble point values of the letters in the US spelling of the numbers in the deck.
  
• [38, 82, 84] slots never touched by Ace, 5, or 9 in perfect out-shuffles of standard 52 card decks, mod 52

Felissan has:

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

NotMySpamAccount has:

• [2, 4, 32] {
  2ⁿ
  } powers of two

StrangerCoug has:

• [17, 19, 43] primes

It is Felissan's turn

[Plotinus]

Felissan has been prodded. It will be NotMySpamAccount's turn in (expired on 2019-10-04 18:50:00) or as soon as Felissan posts, whichever comes first.

[Felissan]

I add 256 to NMSA's powers of 2.

[NotMySpamAccount]

73, 13 to implo's 2 digit odds

[StrangerCoug]

Play [51, 55] to finish the 2-digit odds

[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

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

Implosion has 7 points and:

DeathRowKitty has:

• [8, 18, 34] n is the sum of the Scrabble point values of the letters in the US spelling of the numbers in the deck.
  
• [38, 82, 84] slots never touched by Ace, 5, or 9 in perfect out-shuffles of standard 52 card decks, mod 52

Felissan has:

• [4, 20, 36] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [2, 4, 32, 256] {
  2ⁿ
  } powers of two

NotMySpamAccount has:

StrangerCoug has 7 points and :

• [17, 19, 43] primes

It is McMenno's turn

[McMenno]

numbers that, when their digits keep being added together, make an odd number
23 (-> 5)
46 (-> 10 -> 1)
59 (-> 14 -> 5)

[implosion]

I'll take that and complete it with 10, 70, 45, 21.

[DeathRowKitty]

add [6, 7, 13, 20, 24, 40] to scrabble sequence

Example numbers for which those numbers are the Scrabble point values:

6: two
7: four
13: fifteen
20: twenty-three
24: fifty-five
40: one hundred sixty-five

[Felissan]

Oh come on, I was building up to stealing it

[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.

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

Implosion has 14 points and:

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:

• [4, 20, 36] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [2, 4, 32, 256] {
  2ⁿ
  } powers of two

NotMySpamAccount has:

StrangerCoug has 7 points and :

• [17, 19, 43] primes

It is Felissan's turn

[DeathRowKitty]

Oh come on, I was building up to stealing it

git gud

[Felissan]

I play 30, 40 and 55 as numbers that can be written as 25 + 5N, where N is a triangular number.

Only the Chosen One will be able to complete this sequence.

[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.

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

Implosion has 14 points and:

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:

• [4, 20, 36] {
  16n + 4
  } remainder is 4 when dividing by 16
  
• [2, 4, 32, 256] {
  2ⁿ
  } powers of two
  
• [30, 40, 55] {
  25 + (5n * (n + 1) / 2)
  } 25 + 5n, where n is a triangular number

NotMySpamAccount has:

StrangerCoug has 7 points and :

• [17, 19, 43] primes

It is NotMySpamAccount's turn