[math-fun] Question about uniform distribution (mod 1) of a sequence

Question: Let Q(n) := exp(pi*sqrt(n)) for n = 1,2,3,…. What can be said about the distribution of the sequence frac(Q(n)) = Q(n) (mod 1) ??? Since my next birthday, #n, satisfies exp(pi*sqrt(n)) is close to an integer, I was wondering what the sequence (letting f(x) := min{frac(x),1-frac(x)} be the distance of x to its nearest integer): n_1 = 1, and n_(k+1) := min{n | f(Q(n))) < f(Q(n_k))} looks like. I.e., n for which f(Q(x)) is a record low. —Dan