  We exploit results from the classical Stieltjes moment problem to bring out
the totality of all the information regarding phase insensitive nonclassicality
of a state as captured by the photon number distribution p_n. Central to our
approach is the realization that n !p_n constitutes the sequence of moments of
a (quasi) probability distribution, notwithstanding the fact that p_n can by
itself be regarded as a probability distribution. This leads to classicality
restrictions on p_n that are local in n involving p_n's for only a small number
of consecutive n's, enabling a critical examination of the conjecture that
oscillation in p_n is a signature of nonclassicality.
