08/01/2014, 01:53 AM

(07/31/2014, 01:51 AM)jaydfox Wrote: If we take k very high, the continuous function seems to converge on a constant multiple of the discrete sequence. I'm not sure what to make of this constant yet, but I assume it has an interesting interpretation. Based on analysis of the first 2^18 terms in the sequence, the constant is somewhere between 1.083035 and 1.083089, and probably pretty close to the center of that interval, about 1.083062.

I did some googling, and I found this reference:

http://link.springer.com/article/10.1007/BF01933448

I can't read the whole article, but when I was googling 1.083063 (going to 2^21 terms showed this as a slightly better approximation), I found this (the link is the article above):

So I'm hoping that if someone could get access to that article, they might be able to shed a little light on this constant factor.

~ Jay Daniel Fox