Monday, July 15, 2024

Khinchin geometric means

I first did a geometric-means analysis for Khinchin's constant (K) in early 2000 using 110000 decimal digits of the number. Late Friday, Neil Sloane informed me that a Carlos Simó had calculated one million digits! Converting these to 969680 continued-fraction terms, I did a reanalysis:

click to enlarge

In this range, the final time that the mean changes sign is from (540114, -9.67033*10^-7) to (540115, 0.0000323051). The record (proximity to K) mean at 353014 is -4.14662*10^-9.

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