You are undoubtedly looking for Vice President Joe Biden. However this is nothing more than an urban myth. President Obama became President at noon on the day of his inauguration, regardless of whether or not the oath contained an error.
Only four terms? That's the most any one president has served. Franklin Delano Roosevelt served three terms, starting in 1933, and died during his fourth term in 1945. Every other President has only served one or two terms.
The first US president to only serve one term would be John Adams. He was the second president of the country, and he was the first Vice President of the country under Washington. He was defeated for reelection by Thomas Jefferson, so he only served one term as President.