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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