  We find new static, spherically symmetric, and asymptotically flat vacuum
solutions without horizon in Starobinsky's quadratic f(R) gravity. We
systematically classify these solutions by an asymptotic analysis around the
origin and find seven different integer Frobenius families. We numerically
solve the exact equations of motion by a double-shooting method and specify
boundary conditions by matching the numerical solution to the analytic solution
of the linearised field equations in the weak field regime. We find that all
integer Frobenius families can be connected to asymptotically flat solutions
and trace out lines in the parameter space, allowing to ultimately relate all
free parameters to the total mass at infinity.
