Sequencer | StrangerCoug's turn

[Plotinus]

Yimmy has requested replacement and Jackal711 has confirmed he's still interested, so it is now Jackal711's turn.

Edit: let's have this on this page, too

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

Analysis (NotAJumbleofNumbers, Micc) has 8 points:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [20, 35, 79] {
  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 }
  
• [15, 32, 66] {
  n = 2ⁱ ± 2^j
  } numbers that can be written as the sum or difference of two powers of two

Algebra (StrangerCoug, Jackal711) has:

• [1, 3, 5] {
  n < 10
  } single digit numbers
  
• [16, 20, 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 }

It is

Jackal711's

turn

[Jackal711]

Hmm not much I can do with this hand..

Play [69, 72, 78]
as "numbers whose sum is a multiple of 3"

[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

Analysis (NotAJumbleofNumbers, Micc) has 8 points:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [20, 35, 79] {
  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 }
  
• [15, 32, 66] {
  n = 2ⁱ ± 2^j
  } numbers that can be written as the sum or difference of two powers of two

Algebra (StrangerCoug, Jackal711) has:

• [1, 3, 5] {
  n < 10
  } single digit numbers
  
• [16, 20, 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 }
  
• [69, 72, 78] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 3 | Σ_i∈[0,d]a_i; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers whose sum is a multiple of 3

It is

NotAJumbleofNumbers's

turn

This sequence has another closed form that looks very different from this one, but I wanted to match the verbal form as closely as I could

[Plotinus]

NotAJumbleOfNumbers has been prodded and has another (expired on 2019-12-17 03:53:25) to go before I start looking for a replacement.

[NotAJumbleOfNumbers]

Play 32, 94, 120 to steal [16, 20, 200].

[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

Analysis (NotAJumbleofNumbers, Micc) has 8 points:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [20, 35, 79] {
  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 }
  
• [15, 32, 66] {
  n = 2ⁱ ± 2^j
  } numbers that can be written as the sum or difference of two powers of two
  
• [16, 32, 20, 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

Algebra (StrangerCoug, Jackal711) has:

• [1, 3, 5] {
  n < 10
  } single digit numbers }
  
• [69, 72, 78] {
  n = a₀10^d + a₁10^d-1 + ... + a_d10⁰ with 3 | Σ_i∈[0,d]a_i; a_i ≥ 0, d > 0; k ∈ ℤ
  } numbers whose sum is a multiple of 3

It is

StrangerCoug's

turn

[StrangerCoug]

Play 165, 576, 6, 42, 27, and 21 to claim the numbers whose digit sums are multiples of 3

[Micc]

Play 4, 8, 9, 20 and 80 to claim numbers that can be written as the sum or difference of two powers of two.

[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

Analysis (NotAJumbleofNumbers, Micc) has 16 points and:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [20, 35, 79] {
  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, 32, 20, 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

Algebra (StrangerCoug, Jackal711) has 9 points and:

• [1, 3, 5] {
  n < 10
  } single digit numbers }

It is

Jackal711's

turn

Now that it's done, some other ways of writing the closed form for digit sums are multiples of 3 is

3n

, or

n % 3 == 0

or

3 | n

. I'm replacing the closed form in the completed sequences spoiler to make it easier to see which sequences are taken

[Plotinus]

Jackal has been prodded and has another (expired on 2019-12-19 02:59:21) to move before I start looking for a replacement.

I know some holidays are coming up so I was thinking that starting Monday I'd still prod people as needed but I wouldn't start looking for replacements until Friday or something? And then a similar arrangement between December 30 and January 2.

[StrangerCoug]

Sounds good

[Jackal711]

My apologies for the delay, due to RL issues I've had very little free time and no internet access since shortly after my last post.

...and the play I was going to make is invalid. Recalculating...

[Jackal711]

I'll add [6, 9] to single digit numbers

[Jackal711]

Also warning in advance I will be away with likely no access from the 23rd to 26th as I'm going out of town to visit family for Christmas

[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

Analysis (NotAJumbleofNumbers, Micc) has 16 points and:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [20, 35, 79] {
  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, 32, 20, 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

Algebra (StrangerCoug, Jackal711) has 9 points and:

• [1, 3, 5, 6, 9] {
  n < 10
  } single digit numbers }

It is

NotAJumbleofNumbers's

turn

[Plotinus]

Would a longer prod schedule work better for your internet access issues, Jackal? We could switch to 48/24 like a mafia game if that would be easier for everyone

[Plotinus]

Prodded NotAJumbleOfNumbers. They have another (expired on 2019-12-21 04:10:40) to move before I start looking for a replacement.

[NotAJumbleOfNumbers]

/replace

[Micc]

bump for visibility!

[Plotinus]

Finally occurred to me to edit the thread title.

Feel free to PM your friends who might be interested

[Not_Mafia]

/in

[Plotinus]

yay, welcome! It's now Not_Mafia's turn.

[Not_Mafia]

13, 35, 300 for all contain a treble letter when written in Roman numerals

[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

Analysis (Not_Mafia, Micc) has 16 points and:

• [16, 76, 676] {
  n ≡ 6 (mod 10)
  } numbers that end in 6
  
• [20, 35, 79] {
  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, 32, 20, 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
  
• [13, 35, 300] contains a treble letter when written in Roman numerals

Algebra (StrangerCoug, Jackal711) has 9 points and:

• [1, 3, 5, 6, 9] {
  n < 10
  } single digit numbers }

It is

StrangerCoug'ss

turn

Yay, we're back in session

[StrangerCoug]

97, 441, 225, 90: Numbers whose digit sum is a perfect square