2005-11-02, 05:33 | #1 |
Jun 2003
3·23^{2} Posts |
An interesting series
I have been playing with this series, the numbers in the series have been very easy to factor.
Here is how to generate the series. Let t(n)!= t(n)*t(n-1)*t(n-2)...t(0) Start with seed s=t(0) t(1)=smallest factor of (s^2+1) that is already not in the series t(2)=smallest factor of ((s+t(1)!)^2+1) that is already not in the series t(3)=smallest factor of ((s+t(1)!+t(2)!)^2+1) that is already not in the series and so on. Now the question is that for say seed s=1, do you ever run out of the new terms to add in the series. Can it be proven that you never run out of factors for a random s? Any solutions? A similar problem! (Series 2) Start with seed s=t(0) t(1)=smallest factor of (s^2+1) that is already not in the series t(2)=smallest factor of ((s+t(1))^2+1) that is already not in the series t(3)=smallest factor of ((s+t(1)+t(2))^2+1) that is already not in the series and so on. For what seeds will you run out of factors and for which you never run out of factors. For seed=1,2 you do. Citrix |
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