HAx1 is the same as those listed above - it's also Singer 2020. Seems each Mfg likes to use their own system of measurement.
Being that your machine is a White from the 50's, it's most likely Japanse made, and would take "Singer size" needles. It's interesting that before WW2, only a few US machines used the Singer needles and side clamp attachments, but after the war and the Japanse companies using the Singer patents - they all ended up using side clamp and the same size needle.
There were a few US companies that had switched to useing the shorter needle prior.
Pfaff and Viking used the side clamp and shorter needle - I don't know which used it first, one of these or Singer. Makes you wonder if these three had ties from way, way back . . . they are all owned by the same company today.