Now I'll never know why all those squares were there...

Can I ask how you figured it out?

It's hard to have something simultaneously cool and not google-able.

@ghug- Once I assumed there were two steps to it it came quickly. Basically, all of the numbers were a product of 4 primes. This is super unlikely to be a coincidence (although I guess it sorta ended up being so). So really the only way that the numbers could have been modified is multiplicatively, and they don't share any factors. An early guess was that the multiplication was by successive primes (good theming there) and then I recognized the number 541, as I've done a decent amount of number theory in my life.

Ok, here is my sequence. It's similar to a truly beautiful sequence that I wanted to use, but that one is immediately google-able. Not sure if it has any deep mathematical meaning like the one I wanted to use, though. I think it is very possible to reason it out, though. Here it is:

1, 4, 16, 28, 112, 448, 784

3136 12544 21952?

I *think* that is wrong, but if you have a good explanation for it, then it's as good as any answer.

Your sequence proceeds (so far as it goes) as follows: multiply by 4 twice in a row, then multiply by 1.75:

1, 4 = 4*1, 16 = 4*4, 28=1.75*16, 112=4*28,448 = 4*112,784 = 1.75*448.

I wouldn't go as far as saying that that is a coincidence, but it doesn't persist later into the sequence. I'll add two more numbers:

1, 4, 16, 28, 112, 448, 784, 3136, 12301

Sure, just ruin a nice pattern with a prime.

Next numbers are 19684, 78736, 314944

Done by converting numbers to ternary and building a little tree out of them, where the digits are generated as the sum of their "parents", mod 3.

In ternary, the sequence given is 1, 11, 121, 1001, 11011, etc...

You can space out the pyramid yourself HTML formatting will make this hard to see:

1
1 1
1 2 1
1 0 0 1
1 1 0 1 1
1 2 1 1 2 1
1 0 0 2 0 0 1
1 1 0 2 2 0 1 1
1 2 1 2 1 2 1 2 1
1 0 0 0 0 0 0 0 0 1
1 1 0 0 0 0 0 0 0 1 1
1 2 1 0 0 0 0 0 0 1 2 1

Oh right so in ternary 19684 = 1 0 0 0 0 0 0 0 0 1, 78736 = 1 1 0 0 0 0 0 0 0 1 1, 314944 = 1 2 1 0 0 0 0 0 0 1 2 1

Сетунь FOREVER LONG LIVE TERNARY COMPUTING!

"DSSP was not invented. It was found. That is why DSSP has not versions, but only extensions. Forth is created by practice. DSSP is created by theory. It is not a word."

^Yeah, that's right. I chose the sequence because the analogous thing with binary describes the first 31 odd regular polygons one can construct using a compass and a ruler, which is a pretty cool corollary of a result first conjectured by Fermat and can be proved pretty elegantly with Galois theory.

Shit now I gotta think of something gimme a minute...

OK, how's this

2, 9, 30, 70, 165, 273...

476, 684?

@ghug yes, please explain and make it official!

Anyways, yes, ghug got it, I gotta go...

nth term is the nth triangle number times the nth prime

3, 4, 7, 10, 18, 25, 32

Yes indeed ghug

Threads like these both remind me why I dropped Math and make me feel dumb for it.

Threads like these remind me why I'm taking advantage of a loophole in my school's curriculum to get out of taking a single math class during the next four years.

@bo_sox48 Take the math classes. If you switch into STEM stuff later it's a nightmare trying to catch up. DON'T BE LIKE TENDMOTE WAS!

It's a nightmare no matter when you do it. Besides, I've already ruled out three of the four letters in that horrible acronym, and the only subfield of the fourth letter that I haven't ruled out yet that I'm considering requires less than I already took in high school.

@bo

Weren't you thinking of doing bio?

Taking bio classes, sure, but not as a major.

If you're interested in actually working in a biology field, CS courses would do you a world of good with the recent wave of bioinformatics.

Literally the only thing I would do with a biology major is go work as a ranger somewhere where the nearest place to get bars for your phone is over a hundred miles away in any direction.