After WWII Germany was prohibited from making motorcycles until 1948. In 1948 through 1950 BMW produced what were essentially pre war motorcycles. In 1951 they introduced the 51/3, their first entirely new bike after the war.
The 51/3 was sold for for 5 years, and there were no changes of note across the entire production run.
The 51/3 sported a 494 cc (30.1 CID) OHV boxer twin that pushed 24 HP through a shaft drive to a bike that weighed 419 pounds. Top speed was said to be 87 MPH.
You can find this piece of BMW history in Beavercreek, OH for sale here on Cycle Trader at $13,500. Judging by the amount of work done and the quality of the bike and hack the price seems quite fair.