What number comes next and why?

The answer to this is 65511


Why indeed, I will wait to see if anyone (Mark) agrees

I don't have a clue.

Whoops, I almost forgot about this.


It's complicated to detail the method for achieving the answer, so bear with me please...

Let n be the position in the sequence, and R(n) be the answer - so in this case R(1)=1, R(2)=3, R(3)=5 etc.

Also, let X(n) be the sequence of prime numbers: X(n)=1, 2, 3, 5, 7, 11, 13, 17 etc

Okay - let Y(n) be X(n+1) - X(n).
So Y(n) = 1, 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6 etc.

And thus Y(n)-2 = -1, -1, 0, 0, 2, 0 , 2, 0 , 2, 4 etc

Now let D(n) be the SUM of ALL {Y(n)-2} from n=0 to n

i.e. the sequence D(n) = -1, -2, -2, -2, 0, 0, 2, 2, 4, 8 etc.

The solution is thus:
R(n) = 2^(n-1) - D(n) - 1.

So, when n=6, 2^(6-1) = 32; D(n) = 0; so R(6) = 32 - 0 - 1 = 31.

When n=12, 2^(12-11) = 2048; D(12) = 12; so R(12) = 2048 - 12 - 1 = 2035.

Likewise, when n=17 (i.e. the next in the sequence):
2(n-1) = 2^(17-1) = 65536; D(17) = 24; so R(17) = 65536 - 24 - 1 = 65511.


The only difficulty is in working out D(n). However, I'll leave that to you.

"Also, let X(n) be the sequence of prime numbers: X(n)=1, 2, 3, 5, 7, 11, 13, 17 etc"

But one isn't prime. Where in hell did you come up with that?

I am completely baffled as to how anyone could ever figure that out.

Here is a link to the online dictionary of integer sequences: http://www.research.att.com/~njas/sequences/

it's always surprising to see a sequence not included in the dictionary, so you should send it in.

This one seems rather contrived.

How about this one. What should come logically on the question marks


[1/2 1/2] [1/4 1/2 1/4] [ ??? ] [1/8 1/4 1/4 1/4 1/8]

How about
1/6 1/3 1/3 1/6

The Fibbonacci
Haven't you guess seen the Da Vinci Code? It talks about teh Fibbonacci Sequence. All you have to do is do it in a different matter though. So the answer is...I don't know, because that isn't the fibbonacci. Oh well. And i hate fractions. I don't like them, well, except for some things. Just not this.

or maybe [1/8 1/8 1/2 1/8 1/8]

genius!...

so is it correct then?

ooooo oooo i like pokemon i like pokemon!!!!!!!!!

algorithms... yawn.