- --- In primenumbers@yahoogroups.com,

"John" <reddwarf2956@...> wrote:

> a := sum ({n,1,k}, prime_n^(1/n) prime_(n+1)^(1/(n+1)))

which was an unhelpful way of defining

a(k) = 2 - prime(k+1)^(1/(k+1))

At large k, the PNT gives

(1 - a(k))*log(k)/k = 1 + O(log(log(k))/log(k))

David - --- In primenumbers@yahoogroups.com,

"djbroadhurst" <d.broadhurst@...> wrote:

> a(k) = 2 - prime(k+1)^(1/(k+1))

but meant to write

> (1 - a(k))*log(k)/k = 1 + O(log(log(k))/log(k))

(1 - a(k)) = (log(k)/k)*(1 + O(log(log(k))/log(k)))