So I was having a dream and suddenly started wondering about various properties of exponential growth. Yes I am drop dead serious. After waking up, this is what I came up with. For bonus points see if you can guess the functions used to create these numbers.

2

6

42

1806

3263442

3

5

9

17

33

65

129

257

513

4

10

22

46

94

190

382

766

1534

## 18.9.09

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f(x)=x*(x+1), f(x)=(x*2)-1, f(x)=(2*x)+2

ReplyDeleteI usually dream about random stuff or about char creation for my current MMO. :> I guess this is what I will be doing tonight. I am not sure if I want pale or purple skin! ;)

BTW: I wonder why you dream about that. And why I tried to solve it, I have not touched a function in years.

Well, this particular dream also involved what could only be described as "Space Station Second Life" and, the part that woke me up, having a tarantula the size of a dinner plate on my back. But at one point the Applied Phlebotinum of the dream was the use of exponential numbers, so I woke up thinking about ways to play with the concept.

ReplyDeleteAn interesting note, the second group was actually made using f(x)=(x^2)+1, but yours also works perfectly, which is pretty awesome. I keep thinking I'd probably have had more fun in math class if it had consisted of playing around like this.

@HooUzo just told me that (x^2)+1 does not work. 1^2 + 1 is not 3, but 2. But he can explain you all this on Twitter. I personally had enough math for tonight. :)

ReplyDeleteahh, right, I put those in the wrong order, that should have been (2^x)+1 not (x^2)+1.

ReplyDelete