Random sequential addition is a process that generates nonequilibrium configurations of hard objects. The corresponding spatial pair correlations are investigated via a Percus-Yevick (PY)-like integral equation. Numerical solutions are obtained in one, two, and three dimensions. Comparison with exact results in one dimension and with Monte Carlo data in higher dimensions shows that the PY-like integral equation provides an accurate description of the structure, except close to the jamming limit, where the logarithmic divergence of the correlation function at contact is not reproduced. Using diagrammatic expansions, we show that in one dimension, contrary to its equilibrium counterpart, this equation is only exact up to the second order in density.