New sequence : Primes for which SQRT(A000040(n)) < A001223(n)

[Dean Hickerson]

Mostly to David Wilson:

Concerning primes p for which there are no primes between p and p+sqrt(p),
you asked:

> Wouldn't the finiteness of this sequence follow from the prime number 
> theorem? 

Not that I can see.  Do you have a proof?

Note that finiteness of this sequence implies that, for every sufficiently
large positive integer n, there's a prime between n^2 and (n+1)^2.  Except
for the "sufficiently large", that's Legendre's conjecture, which is still
unproved.

Dean Hickerson
dean at math.ucdavis.edu