100, 100, 67, 75, 40, 67, 29, 50, 33, __

40

Don't know

1:56




PairTheBoard

-7157

G[x]= -1177/13440*x^8 + 35123/10080*x^7 -167533/2880*x^6 +
381133/720*x^5 -16432157/5760*x^4 +
13314101/1440*x^3 -175441757/10080*x^2 + 4793673/280*x -6483

G at 1,2,3,4,5,6,7,8,9 is 100,100,67,75,40,67,29,50,33 and at 10 it is -7157 lol

Point being that i dont care what the next number is. Its what i say it is if i can find a pattern however ridiculous lol.

spoilers guys, geeze. I don't see a worthwhile pattern here.

No need for spoiler because i know it's not what i posted. I meant it's whatever pattern you can create if it gets too obscure for the easy ones.

For any number that one could say is the next number in the sequence there's a rule that would determine that as the next number.

The numbers tend to become smaller on average when going from left to right.

Maybe it's indeed 40.

Yeah, as Tom posted earlier, I agree that the answer is 40. I'll post the formula later today.

SMP (spoilered my post)

Zero, zero.

Thanks to OP fernword for a nice puzzle diversion. Don't look at the the spoiler if you want to continue trying to solve the sequence on your own. I believe this is the simplest solution to the sequence.

Nice job. Thanks to everyone who gave it a try.

This is pretty much as far as I got.

Bravo

Still thinking



I'm going to have to take a rain check.

Masque - how did you do this? Some kind of program? I didn't realize at first that G(x) actually produces the numbers in my sequence. It's amazing.

Any sequence of numbers can be fit to a polynomial of sufficient degree. I'm sure that was automated, but you can solve it as a system of equations (a*1^8 + b*1^7...=N_1, a*2^8 + b*2^7...=N_2) if you're really bored.

Okay, this made me laugh and spill coffee on my desk.

Playing with polynomials was a favorite pastime of mine years ago when taking college math classes. But I noted the bolded - my intuition tells me that the sequence of prime numbers can't be fit to a polynomial expression. But then I think you imply that "any sequence " is non-random repeatability, thus reducible to polynomial expressions. But then is the sequence of prime numbers non-random? I'm probably out of my element here - perhaps lastcard, Masque or this guy Tom can provide some illumination.

You can fit any number of primes you want to a polynomial and even make it fit the prime number function Prime[n] that gives you the nth prime up to a point.

But it is a good question if it can be proven that any number of these are true;

1) Can you find a polynomial in integer coefficients from N to N that produces infinite number of primes?

2) Can the prime number function be given by a polynomial?

This second is not possible because of prime number theorem. Eventually for large n a polynomial will deliver terms that are separated by such big gaps that will violate the prime number counting function (ie how many primes up to number n goes like n/log(n))


Here is a miracle polynomial that for its first 40 values of n 0 to 39 gives only primes;

n^2+n+41

But obviously n=41 will not work and any n=41*k argument will not deliver prime.

You can use that argument in general to show that a polynomial with a constant term a(0) will deliver a composite number when evaluated at any z*a(0) value. If it doesnt have a constant term it is always giving composites for any x