The source from which I got the information didn't include a pension-application number, but I appended a note saying that it was probably S1893. The information that I copied about the person is below.
William AlexanderMauryPrivate, North Carolina Line, $60.00 Annual Allowance $150.00 Amount Received March 9 1833 Pension Started Age 74 (1835 TN Pension Roll)
The age and most appear correct for my William, but he was apparently not if his wife was Elizabeth Sturgeon, unless she was a second wife. My William's first wife was Esther or Easter (sometimes spelled one way, sometimes the other).