Random posts

[Saka]

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.

[Bullet51]

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.

[calcyman]

EDIT: How to type in subscripts and superscripts? The p_n here means p(subscript)n.

Surround the equation in dollar-signs, LaTeX-style.

[Saka]

All Levels of Sandbox:
Sandbox I
Sandbox II
Sandbox III
Sandbox IV
Sandbox V
Sandbox VI
Sandbox VII
=====FALSE SANDBOXES*=====
Sandbox VIII
Sandbox IX
Sandbox X
Sandbox XI
Sandbox XII
Sandbox XIII
Sandbox XIV
Sandbox XV
Sandbox XVI
Sandbox XVII
Sandbox XVIII
Sandbox XIX
Sandbox XX
Sandbox XXI
Sandbox XXII (Plausible)

*These are not true sandboxes; we are not allowed to freely modify and create things in these "sandboxes".

[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.

[dani]

⃰

[dani]

⃰

it doesn't work when you quote it though. :^(

[cordership3]

https://catagolue.appspot.com/census/b3s23/C1

[lifeisawesome]

My only great-grandmother was born 2 days before John Conway.

[Saka]

My only great-grandmother was born 2 days before John Conway.

Wow you only have 1 great grandmother?
Then how do you exist?

[KittyTac]

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".

[gameoflifemaniac]

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!

[gameoflifemaniac]

some...
































































































































































































BODYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY WUNCE TULDD MEH dA WWWOLRD Iis GONQAN RUOL mEmE

[googleplex]

I have only one living great-grandmother, too!

So do I, but she's dying...

[gameoflifemaniac]

I have only one living great-grandmother, too!

So do I, but she's dying...

I feel sorry...
How old is she?

[Saka]

I have 0 living great grandparents

[gameoflifemaniac]

I have 0 living great grandparents

nothing to say...

[cordership3]

I got my first unix in a while, and saw this...

[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).

[Goldtiger997]

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.

I see no simple patterns

Here's one:
21978*4
219978*4
2199978*4
21999978*4
219999978*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

[AforAmpere]

Wow, this is my 500th post. I didn't realize it would happen so quickly.

[cordership3]

And this is my 40th post.

[Majestas32]

And this is my 301st

yey 301

[Saka]

blah blah blah

I saw what you did there...

[Goldtiger997]

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.