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Re: Pseudorandom posts
Posted: March 3rd, 2018, 3:58 am
by Saka
Goldtiger997 wrote:I see no simple patterns
Here's one:
21978*4
219978*4
2199978*4
21999978*4
219999978*4
219999999978*4
etc.
Also applies to 1089:
10989*9
109989*9
1099989*9
10999989*9
etc.
Re: Random posts
Posted: March 3rd, 2018, 7:57 am
by Bullet51
Goldtiger997 wrote:Let pₙ denote the nth prime.
Prove that for all real h > 1, there are infinitely many integers n such that pₙ < nʰ.
Suppose that there are only finitely many integers n such that pₙ < nʰ, that is to say, there is a largest integer m such that pₘ < mʰ.
Thus the
sum of the reciprocals of the primes can be written as
1/p₁+1/p₂+1/p₃+...+1/pₘ+(1/pₘ₊₁/pₘ₊₂+...)
which is less than
1/p₁+1/p₂+1/p₃+...+1/pₘ+(1/Mʰ+1/(M+1)ʰ+...)
which converges if h > 1.
But the sum of the reciprocals of the primes diverges. Contradiction.
Re: Random posts
Posted: March 3rd, 2018, 8:25 am
by apg
Bullet51 wrote:EDIT: How to type in subscripts and superscripts? The p_n here means p(subscript)n.
Surround the equation in dollar-signs, LaTeX-style.
Re: Random posts
Posted: March 3rd, 2018, 8:56 am
by Saka
Re: Random posts
Posted: March 3rd, 2018, 9:37 am
by Bullet51
Equation Test
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)
EDIT: It's just unicode magic.
I made an invisible message without using bbcode
Posted: March 3rd, 2018, 1:17 pm
by dani
⃰
Re: I made an invisible message without using bbcode
Posted: March 3rd, 2018, 1:18 pm
by dani
danny wrote:⃰
it doesn't work when you quote it though. :^(
ten cento per ŸÊÂR is all i nEed
Posted: March 4th, 2018, 10:20 pm
by cordership3
Re: Random posts
Posted: March 5th, 2018, 8:18 am
by lifeisawesome
My only great-grandmother was born 2 days before John Conway.
Re: Random posts
Posted: March 5th, 2018, 9:19 am
by Saka
lifeisawesome wrote:My only great-grandmother was born 2 days before John Conway.
Wow you only have 1 great grandmother?
Then how do you exist?
Re: Random posts
Posted: March 5th, 2018, 9:23 am
by KittyTac
Saka wrote:lifeisawesome wrote:My only great-grandmother was born 2 days before John Conway.
Wow you only have 1 great grandmother?
Then how do you exist?
He/she probably meant "my only great-grandmother who is still alive".
Re: Random posts
Posted: March 5th, 2018, 12:42 pm
by gameoflifemaniac
KittyTac wrote:Saka wrote:lifeisawesome wrote:My only great-grandmother was born 2 days before John Conway.
Wow you only have 1 great grandmother?
Then how do you exist?
He/she probably meant "my only great-grandmother who is still alive".
I have only one living great-grandmother, too!
Re: Random posts
Posted: March 5th, 2018, 12:48 pm
by gameoflifemaniac
some...
BODYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY WUNCE TULDD MEH dA WWWOLRD Iis GONQAN RUOL mEmE
Re: Random posts
Posted: March 5th, 2018, 1:04 pm
by googleplex
gameoflifemaniac wrote:
I have only one living great-grandmother, too!
So do I, but she's dying...
Re: Random posts
Posted: March 5th, 2018, 1:31 pm
by gameoflifemaniac
googleplex wrote:gameoflifemaniac wrote:
I have only one living great-grandmother, too!
So do I, but she's dying...
I feel sorry...
How old is she?
Re: Random posts
Posted: March 5th, 2018, 7:56 pm
by Saka
I have 0 living great grandparents
Re: Random posts
Posted: March 6th, 2018, 2:52 am
by gameoflifemaniac
Saka wrote:I have 0 living great grandparents
nothing to say...
Re: Random posts
Posted: March 7th, 2018, 9:43 pm
by cordership3
I got my first unix in a while, and saw this...
Re: Random posts
Posted: March 7th, 2018, 10:45 pm
by 77topaz
CGoL mathematics: the number of unique snake-carrier chain still lifes with 6+4N cells (N≥0) =
OEIS A005578(N+2).
e.g. for N=1 there are three examples:
Code: Select all
x = 27, y = 4, rule = B3/S23
2ob2obo3b2ob2o5b2o$ob2ob2o3bob2o2bo3bo2b2o$15b2o5b2o2bo$25b2o!
EDIT: BlinkerSpawn pointed out on the Discord that I made an arithmetic error; the correct formula is actually
A001405(N+2).
EDIT 2: Nope, that was also wrong, it's
A005418(N+2).
Re: Rαndom posts
Posted: March 8th, 2018, 6:25 am
by Goldtiger997
Bullet51 wrote:Goldtiger997 wrote:Let pₙ denote the nth prime.
Prove that for all real h > 1, there are infinitely many integers n such that pₙ < nʰ.
[a proof by contradiction.]
Nice, that's basically the same method as mine.
Saka wrote:Goldtiger997 wrote:I see no simple patterns
Here's one:
21978*4
219978*4
2199978*4
21999978*4
2199
99978*4
219999999978*4
etc.
Sorry, I wasn't very clear. I was aware of that pattern, but what I was wondering about was the distribution of families in different bases.
A Barbarian Wren's Ivory
Re: Random posts
Posted: March 9th, 2018, 9:33 pm
by AforAmpere
Wow, this is my 500th post. I didn't realize it would happen so quickly.
Re: Random posts
Posted: March 9th, 2018, 9:48 pm
by cordership3
And this is my 40th post.
Re: Random posts
Posted: March 9th, 2018, 10:10 pm
by Majestas32
And this is my 301st
yey 301
Reː Random posts
Posted: March 9th, 2018, 10:16 pm
by Saka
Goldtiger997 wrote:blah blah blah
I saw what you did there...
Re: Randσm posts
Posted: March 9th, 2018, 10:18 pm
by Goldtiger997
Saka wrote:Goldtiger997 wrote:blah blah blah
I saw what you did there...
I believe I did three different things. Which one were you referring to?
Edit: Edit 3: actually I will stop avoiding another post by editing.
Edit 2: just realised this was my 365th post; one for everyday of the year.