We investigate the statistics of isolated recycled pulsars and double neutron star binaries in the Galactic disk .
Since recycled pulsars are believed to form through accretion and spinup in close binaries , the isolated objects presumably originate from disrupted progenitors of double neutron stars .
There are a comparable number of double neutron star systems compared to isolated recycled pulsars .
We find that standard evolutionary models can not explain this fact , predicting several times the number of isolated recycled pulsars than those in double neutron star systems .
We demonstrate , through population synthesis calculations , that the velocity distribution of isolated recycled pulsars is broader than for binary systems .
When this is accounted for in a model for radio pulsar survey selection effects , which include the effects of Doppler smearing for the double neutron star binaries , we find that there is a small ( \sim 25 \% ) bias towards the detection of double neutron star systems .
This bias , however , is not significant enough to explain the observational discrepancy if standard ( \sigma = 265 km s ^ { -1 } ) neutron star natal kick velocities are invoked in binary population syntheses .
Population syntheses in which the 1D Maxwellian velocity dispersion of the natal kick is \sigma \sim 170 km s ^ { -1 } are consistent with the observations .
These conclusions further support earlier findings the neutron stars formed in close interacting binaries receive significantly smaller natal kicks than the velocities of Galactic single pulsars would seem to indicate .