There are five, namely John Adams, John Quincy Adams, John Tyler, and John Calvin Coolidge and John Fitzgerald Kennedy. Coolidge totally dropped his name of "John" soon after he left college. He never went by John.
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No US presidents were named Nathaniel.
None of them had Jack for his legal name. John Kennedy was informally known as Jack Kennedy and even signed his name that way sometimes.
The United States has never had a President with the name of David.
As of June 2014, no United States President has been named Sebastian. The first president was named George. The current president is named Barack.
John Adams and his son John Quincy Adams were US presidents from Mass.