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User talk:Alexei Kourbatov
Alexei - FYI
What do you think?
From: Alexander Povolotsky <apovolot@gmail.com>
Date: May 26, 2016 at 3:07:59 PM EDT
To: Carlos Rivera <cbrfgm@gmail.com>
Cc: rosturco.na@gmail.com
Subject: Interesting?
Hi Dear Carlos,
As posted on my personal oeis wiki page https://oeis.org/wiki/User:Alexander_R._Povolotsky
According to WolframAlpha partial sums
(I actually used the Maple notation for the input)
sum(prime(n)/prime(n+1)/n^2,n=1...infinity)
seems to converge in the vicinity of 1.12984...
P.S. On May 24, 2016, at 7:54 AM, Rosario Turco <rosturco.na@gmail.com>
wrote to me via private email that, following my above observation, he observed
(extrapolating results for k in the range from k=2 to k=50) that:
lim(sum(prime(n)/prime(n+1)/n^k,n=1...infinity), k->infinity) = 2/3
What do you think?
Thanks,
Best Regards,
Alexander R. Povolotsky
On another hand
lim(sum(prime(n)/prime(n+1)/n^k,n=1...infinity), k->infinity) = 2/3
just means that for large enough "k" the above sum degrades to its first additive component
prime(1)/prime(2)/(1)^k = 2/3
