[Guest]

Firstly, my old unsolved sequences:

1) 1, 8, 10.125, 17.58, 26.42, …

2) 0, 4, 11.25, 17.42, 26.44, …

And now the new one :

3) 1, 16, 19683, 429467296, 29802322390000000, …

Just find the 6th number

A hint for the first:

Only squares where used to calculate this.

A hint for the second:

A varient for the first, but the starting number is different. It's zero

And no hint for the third.

[Guest]

I think this is what you are going for:

1^(1*1)=1

2^(2*2)=16

3^(3*3)=19683

4^(4*4)=429467296

5^(5*5)=298023223876953125

6^(6*6)=10314424798490535546171949056

The numbers do not reflect the normal truncation after the first 10 digits. Check out the results with the High Precision javascript Calculator at http://www.petting-zoo.org/Calculator.html

Edited February 16, 2009 by Snowman63

[Guest]

I think this is what you are going for:

1^(1*1)=1

2^(2*2)=16

3^(3*3)=19683

4^(4*4)=429467296

5^(5*5)=298023223876953125

6^(6*6)=10314424798490535546171949056

The numbers do not reflect the normal truncation after the first 10 digits. Check out the results with the High Precision javascript Calculator at http://www.petting-zoo.org/Calculator.html

I was using a TI 84+. It rounded some of them.

And that was indeed the idea.

Any luck on the other two?

[Pickett]

The other two are:

f(n) = n² + n²/f(n-1)

However, technically speaking, the second sequence doesn't work, since

f(1) = 0

f(2) = 2² + 2²/f(1) and f(1) = 0 in this case...so, you're dividing by 0...however, the rest of the numbers work out

So the next two numbers in BOTH sequences is 37.36 (and from then on, the two sequences will have the same numbers)

Edited February 16, 2009 by Pickett

[Guest]

The other two are:

f(n) = n² + n²/f(n-1)

However, technically speaking, the second sequence doesn't work, since

f(1) = 0

f(2) = 2² + 2²/f(1) and f(1) = 0 in this case...so, you're dividing by 0...however, the rest of the numbers work out

So the next two numbers in BOTH sequences is 37.36 (and from then on, the two sequences will have the same numbers)

That is right for the first one, but...

How did you get 37.36?

And the second sequence uses a different formula, where x= {0, and 2, 3, etc.}

[Pickett]

That is right for the first one, but...

How did you get 37.36?

And the second sequence uses a different formula, where x= {0, and 2, 3, etc.}

I got 37.36 by the following:

f(5) = 26.42 (given)

f(6) = 6² + 6²/f(5) = 36 + 36/26.42 = 36 + 1.362604... = 37.36

And it seems like the formula for the second sequence is the same formula, just a different set of possible X values...I mean everything else after that second term uses the same formula as the first...so, that's why I said that...

And I got the same answer for the second sequence because:

f(5) = 26.44 (given)

f(6) = 6² + 6²/f(5) = 36 + 36/26.44 = 36 + 1.361573... = 37.36

[Guest]

I got 37.36 by the following:

f(5) = 26.42 (given)

f(6) = 6² + 6²/f(5) = 36 + 36/26.42 = 36 + 1.362604... = 37.36

And it seems like the formula for the second sequence is the same formula, just a different set of possible X values...I mean everything else after that second term uses the same formula as the first...so, that's why I said that...

And I got the same answer for the second sequence because:

f(5) = 26.44 (given)

f(6) = 6² + 6²/f(5) = 36 + 36/26.44 = 36 + 1.361573... = 37.36

Since you use a diferent formula, the answer differs in decimal places.

In the spoiler is the actual formula I used:

x²+x²/(x-1)²

Thus:

3²+3²/2²=9+9/4=11.25

The difference is decimal places, as I don't divide by the previous number. Instead, I divide by the previous square.

[Guest]

Since you use a diferent formula, the answer differs in decimal places.

In the spoiler is the actual formula I used:

x²+x²/(x-1)²

Thus:

3²+3²/2²=9+9/4=11.25

The difference is decimal places, as I don't divide by the previous number. Instead, I divide by the previous square.

If I am following you right, your original sequence #2 is wrong:

You gave 0, 4, 11.25, 17.42, 26.44

But, you say the formula is: f(x)=x^2+x^2/((x-1)^2)

Then your sequence should be 0, 8, 11.25, 17.78, 26.56, 37.44...

f(2) = 2^2+2^2/(1^2) = 4 + 4/1 = 8

f(3) = 3^2+3^2/(2^2) = 9 + 9/4 = 11.25

f(4) = 4^2+4^2/(3^2) = 16 + 16/9 = 17.78

f(5) = 5^2+5^2/(4^2) = 25 + 25/16 = 26.56...