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Old 2022-09-19, 16:29   #63
mart_r
 
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Dec 2008
you know...around...

22·11·19 Posts
Default Where's the revolution? C'mon, people, you're letting me down!

The "puzzle" with the geometric mean of consecutive gaps can be generalized: for n consecutive gaps the average ratio of the largest gap divided by the smallest gap appears to be as follows (rounded to three decimal places for n>=4):
Code:
 n  r_gm
 1  1
 2  4
 3  8
 4  12.641
 5  17.757
 6  23.249
 7  29.052
 8  35.121
 9  41.423
10  47.928
I'm afraid these numbers will give me headaches.
1.8 n (0.38 + log n) is an asymptotic facsimile for n<=1000, but we want more than this.


What is it that I should ask myself?
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