Exactly.

ghug is too good at this game. His turn to post now.

I posted one on the last page.

Sorry, thought that was part of your answer to the previous question when skimming.

Oh I didn't see it either!

Ah right I guess ghug's series is this, it looked like it was part of the explanation of the previous question (which I didn't completely read :) )

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

Hmm I'm stumped anyway... does the answer arise from properties of the numbers themselves (in which case I'll keep mulling it over) or does it simply match an obscure sequence only a math major would recognize (I was not a math major!)

I can't think of anything which can account for that 25. It really screws the rest up :(.

It's not as weird as the Carmichael numbers were. There's a little sequence funkiness meant to mess with people, but it should be gettable.

Next is 52.

What were you thinking, HR?

I think it has been 24 hours by now, but I just started to look at it now. Here are my elementary thoughts for those that are interested:

3, 4, 7, 10, 18, 25, 32, 52
The first and third numbers are prime numbers, and everything else is all non-primes. Factored out we get:
(3), (2x2), (7), (2x5), (3x3x2), (5x5), (2x2x2x2x2), (2x2x13)
The things that stand out to me are all of the twos and fives. You also have some squares or multiples thereof. No clear pattern with any of those though.

Looking at the increments in between numbers doesnt really yield anything as well:
+1, +3, +3, +8, +7, +7, +20
Always increasing, but not at a steady rate, and both concave and convex. No leads to go on when I look at that.

The first three numbers made me think of some sort of fibonacci sequence (3+4=7), but again, it doesn't really work after the first couple of numbers in any way I can see.

These are all pretty elementary observations, but I dont really know where else to look, or how else to look at it, so I am pretty stumped right now.

One other thing I am looking at is an 'every other sequence' where it is two sequences put together with every other number. This would give us the sequences:
3, 7, 18, 32
4, 10, 25, 52
Looking at the first list, the differences dont really mean anything (4, 11, 14)
Looking at the second list, the differences are all multiples of three (6, 15, 27)
I dont think that this is an 'every other sequence' though.

Just thinking out loud, nothing to see here.

Wait, I think I may have figured it out... if this is right, then I totally missed something obvious. Here are the next couple numbers:
70, 88, 138, 170, 202
Is that right??

Bumped to see if Squigs is right.

Nope.

59, 94?

Bump!?

I think it is time for ghug to reveal the pattern.

It's the Mersenne exponents (all of which are prime) plus the Fibonacci numbers.

Meh... as such you'd need more information than just the sequence to have figured it out (i.e. you'd have to know what the Mersenne exponents were.) uclabb's question was better, it was all in the sequence :)

I have to say, ghug, I'm not convinced that the Mersenne exponents are a "thing"

So uh, who goes now?

First person to post a question goes! Let's have it!

0, 1, 2, 6, 222

Actually, I'll give you a fifth because that's probably too hard.

0, 1, 2, 6, 222, 2428912878

i don't feel like figuring out the prime factors of 10941049 right now i'm going to bed :/

Factored out you get: (0) (1) (2) (2x3) (2x3x37) (2x3x7x37x43x163x223).
Although I think it is more important to note what each previous number was multiplied by to get the new number: (0) (+1) (x2) (x3) (x37) (x10941049)
Time to research the significance of that large number.

@uclabb, I was in a hurry. I thought it was kind of stupid too. I was hoping someone would figure out the Fibonacci thing because the Mersenne exponents start the same way as the primes do and then go back to try to figure out what sequence of primes those were.

37 is the 1*2*6th prime. Probably doesn't mean anything though.