Silver Ratio based scale

I have applied my latest method for generating PHI scales and found out, sure enough, I was able to get a Silver Ratio-based scale that ALSO intersects the octave perfectly (and almost intersects the 5th perfectly) with this method.

I appears you can throw just about any noble number into this formula and get a scale that closely preserves the 2/1, 3/1, 4/1....harmonics.
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The method is

2.414213 = silver ratio (could also be any other noble number greater than 1)

1 / noble number = 1 / 2.414213 = 0.414213 (generator)

Basic scale is
0.414213
0.1715 = 0.414213 ^ 2
0.07107 = 0.414213 ^ 3

Now add 0.07107 and 0.1715 to get 0.24257
Now add 1 to ALL of the above values
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This gives you the scale
1.07107
1.1715
1.24257
1.414213 (the period)...

....(note that 1.1715 + 1.24257 = 1.414213 and 1.07107 + 1.1715 = 1.24257...a perfect recurring sequence!)

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What does all this have to do with the octave and perfect 5th?
Well....
1.414213 * 1.07107 = 1.51472 (pretty close to a perfect 5th)
And...best yet
!1.414213^2 = 2!
It hits the octave dead-on without any sort of funny tempering needed.
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I also wonder...has anyone else devised such a method to extract scales from noble numbers? Or...can anyone imagine any improvements or uses possible for such scale?

-Michael