Find the missing number in the sequence:

10
11
12
13
14
15
16
17
20
22
24
31
100
?
10000

ebaines, I nscratched my head on this one for a while. But, 10000 is base 2 for 16, 10 is base 16 for 16, and 16 is base 10 for 16.

These are what popped out at me.

Is it 16 in all the bases from base 16 down to base 2?

I doubt it, but I thought I would throw in my 2 cents.

That would mean the missing number is base 3 for 16.

Which is, after using my base conversion program on my TI, 121.

galactus: you got it - I just can't stump you! Each of these is 16 expressed first in base 16, then base 15, then base 14, base 13, etc all the way down to base 2. So the missing number is 16 expressed in base 3, or... 121.

Here's a sequence perhaps you have seen before.

3,3,5,4,4,3,5,5,4,3,

What's the next number?

Here's a sequence perhaps you have seen before.

3,3,5,4,4,3,5,5,4,3,?

what's the next number?.

6

Yes, this is an oldie but goodie.

I have seen that thread of yours, I don't quite remember how I go up to that thread and Capuchin was here then.

If I understood well, your sequence, ebaines, is on the same principle as the 'binary' form, but with different bases, right?

If I understood well, your sequence, ebaines, is on the same principle as the 'binary' form, but with different bases, right?

Yes, different baes. The number 16 can be expresed in any base from 2 on up. So for example in base 15 it's equal to 1 times 15 plus 1, or "11". In base 14 its equal to 1 times 14 plus 2, or "12" etc. So the list is simply the number 16 expressed first in base 16, then base 15, then base 14, then base 13, etc all the way down to base 2.