  We determine the continuum limit of the curvature of the pseudocritical line
of QCD with $n_f$=2+1 staggered fermions at nonzero temperature and quark
density. We perform Monte Carlo simulations at imaginary baryon chemical
potentials, adopting the HISQ/tree action discretization, as implemented in the
code by the MILC collaboration. Couplings are adjusted so as to move on a line
of constant physics, as determined in Ref.~\cite{Bazavov:2011nk}, with the
strange quark mass $m_s$ fixed at its physical value and a light-to-strange
mass ratio $m_l/m_s=1/20$. The chemical potential is set at the same value for
the three quark species, $\mu_l=\mu_s\equiv \mu$. We attempt an extrapolation
to the continuum using the results on lattices with temporal size up to
$L_t=12$. Our estimate for the continuum value of the curvature $\kappa$ at
zero baryon density, $\kappa=0.020(4)$, is compared with recent lattice results
and with experimental determinations of the freeze-out curve.
