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 FeLiNe 2004-04-07 00:38

[QUOTE=biwema]
maybe there is a power, where it takes even longer to meet the first noninteger element...[/QUOTE]

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

[quote]
Since this question was asked, Henry Ibstedt has made extensive calculations,
and found the first noninteger term, x[sub]n[/sub], in the sequence involving [i]k[/i]th 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]
[/quote]

:cat:

 Terrence Law 2004-06-11 02:03

[QUOTE=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?[/QUOTE]

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.

:huh: :coffee: :rolleyes:

 Terrence Law 2004-06-11 02:05

[QUOTE=cheesehead][url]http://mathworld.wolfram.com/GoebelsSequence.html[/url]

"A sequence even more striking for assuming integer values only for many terms is the 3-GĂ¶bel sequence ..."[/QUOTE]

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

:smile: 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.

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