[Guest]

Find the next number in the pattern.

Easy

17, 18, 20, 23, 28, 35, ?

Medium

0, 1, 8, 38, 403, ?

Hard (let's see how long it will take you...)

-4, -3.875, 11,875, 103, 2056.125, 16762.25, ?

If you find that you can't arrive at an answer: 1. Your not good enough at math. or 2. I made a mistake in my math or there is some sort of typo.

Good luck!

[Guest]

Lol, there's no logic for the stuff I do xD. I jut do it and hope it's right :X

I see Well I guess trial and error can work some times.

[Guest]

Will all next numbers in your sequence match to the numbers calculated by my suggested formula?

If there is a difference, could you please tell where?

[Guest]

Will all next numbers in your sequence match to the numbers calculated by my suggested formula?

If there is a difference, could you please tell where?

The number sequence is correct, your just not using the formula I want, but you are close.

[Yoruichi-san]

I think I got it...the third one was throwing me off until I thought of n-parity...

I noticed that the decimal values corresponded to 8ths, so I put them all in terms of 8ths, and the values become: -32/8,-31/8,95/8,825/8,16449/8,134098/8

The differences between the numerators are then: 1=1^6, 126, 729=3^6, 15625=5^6, 117649=7^6

So I was confused since the 2nd transition didn't match (2^6=64) until I realized that -(-31)+64=95, and 2 is the only *even* number in the bunch...

So I think the formula should be as below:

a(i) denotes the ith number in the sequence, starting with i=0 (I start at a(0), that is, -4=a(0), -3.875=a(1), etc)

n(i) denotes the ith prime number, counting 1 (so 1,2,3,5,7,11,etc...)

The formula should be a(i)={[(-1)^(n(i)-1)]*[a(i-1)*8]+ n(i)^6}/8

or formatted to be easier to read(I hope i did it right): a_i = {(-1)^(n_i-1)(a_i-1*8)+n_i⁶}/8

The (-1)^(n(i)-1)=1 for all odd n(i), so it only effects the sign of n(i)=2, which solves that issue...

Anyways, I hope all my parentheses are in the right places, but I get that the next number in the sequence = (134098+11^6)/8=1905659/8 =238207.375

Oh, this also works if you use n(i)+1 or n(i)+3 or n(i)-3 or any n(i)+/-2(integer) instead of n(i)-1 as the exponent...the only thing that matters is the even/odd parity

Nice sequence Data! I'm still working on the one in the newest post...

Edited June 13, 2008 by Yoruichi-san