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User talk:Alexei Kourbatov

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Alexei - FYI

What do you think?

From: Alexander Povolotsky <>

Date: May 26, 2016 at 3:07:59 PM EDT

To: Carlos Rivera <>


Subject: Interesting?

Hi Dear Carlos,

As posted on my personal oeis wiki page

According to WolframAlpha partial sums

(I actually used the Maple notation for the input)


seems to converge in the vicinity of 1.12984...

P.S. On May 24, 2016, at 7:54 AM, Rosario Turco <>

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?


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