Gaps between prime-roots

[Rainer Rosenthal]

In the course of thread "Primes..." in sci.math I proposed
the following:

         1, 113, 1327, ... ???  

where a(n) = smallest natural such that
sqrt(P_(k+1)) - sqrt(P_k) < 1/n  for all k with P_k > a(n)

I don't have a CAS and would be glad to see someone submit 
this sequence with more and better consolidated entries.

As there were no reactions and since this is related to the
OEIS, I send it to all seq-fans.

By the way I want to thank Neil Sloane for his fatherly
care for the OEIS.

Rainer Rosenthal
r.rosenthal at web.de