  Background: Since the first experimental observation, two-nucleon
radioactivity has gained renewed attention over the past fifteen years. The
$^6$Be system is the lightest two-proton ground-state emitter, while $^{16}$Be
has been recently proposed to be the first two-neutron ground-state emitter
ever observed. A proper understanding of their properties and decay modes
requires a reasonable description of the three-body continuum.
  Purpose: Study the ground-state properties of $^6$Be and $^{16}$Be within a
general three-body model and investigate their nucleon-nucleon correlations in
the continuum.
  Method: The pseudostate (PS) method in hyperspherical coordinates, using the
analytical transformed harmonic oscillator (THO) basis for three-body systems,
is used to construct the $^6$Be and $^{16}$Be ground-state wave functions.
These resonances are approximated as a stable PS around the known two-nucleon
separation energy. Effective core-$N$ potentials, constrained by the available
experimental information on the binary subsystems $^5$Li and $^{15}$Be, are
employed in the calculations.
  Results: The ground state of $^{16}$Be is found to present a strong dineutron
configuration, with the valence neutrons occupying mostly an $l=2$ state
relative to the core. The results are consistent with previous $R$-matrix
calculations for the actual continuum. The case of $^6$Be shows a clear
symmetry with respect to its mirror partner, the two-neutron halo $^6$He: The
diproton configuration is dominant, and the valence protons occupy an $l=1$
orbit.
  Conclusions: The PS method is found to be a suitable tool in describing the
properties of unbound $\text{core}+N+N$ ground states. For both $^{16}$Be and
$^6$Be, the results are consistent with previous theoretical studies and
confirm the dominant dinucleon configuration. This favors the picture of a
correlated two-nucleon emission.
