- **Puzzles**
(*https://www.mersenneforum.org/forumdisplay.php?f=18*)

- - **sequence**
(*https://www.mersenneforum.org/showthread.php?t=2301*)

[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: |

[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: |

[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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