sequence

[FeLiNe]

Originally Posted by biwema

maybe there is a power, where it takes even longer to meet the first noninteger element...

Quoting from example 26 in that same article (which was the generalization to powers higher than than 3):

Since this question was asked, Henry Ibstedt has made extensive calculations,
and found the first noninteger term, x_n, in the sequence involving kth powers, to be
[pre]
k 2 3 4 5 6 7 8 9 10 11
n 43 89 97 214 19 239 37 79 83 239
[/pre]

[Terrence Law]

Originally Posted by biwema

Let's define the following sequence:

x[0] = 1

x[n] = ( 1 + x[0]^3 + x[1]^3 + .... + x[n-1]^3) / n

Are all of these sequence integers?

This is a mind-boggling tool and you have to use inequality to draw a line or BEDMAS or asymptotic function. Draw and underline a graph and use subscripts.

Beware, subscript out of range in line 0, write every digit on a square.

[Terrence Law]

Originally Posted by cheesehead

http://mathworld.wolfram.com/GoebelsSequence.html

"A sequence even more striking for assuming integer values only for many terms is the 3-Göbel sequence ..."

Let's use hints and pinpointers and just cheat and look at the answers of the books!

You are smirking!

Just add more references and publish and print the page neatly into a binder and stick it to the wall.

This sequence is challenging, you can write forever, keep writing on foolscap brown paper.