Can a sitting senator run for the other seat?

[RRusso1982]

There is a more recent example of this in North Dakota.  In 1986, Kent Conrad was the Democratic state Tax commissioner running against Republican senator Mark Andrews.  During the campaign, Conrad pledged that if there was still a large budget deficit  in 1992, he would not seek reelection.  In 1992, there was still a large budget deficit so Conrad honored his pledge.  Byron Dorgan won the Democratic primary to replace him.  In September, 1992, Quentin Burdick, the other North Dakota senator, died.  This set up a special election for his seat, which would be up again in 1994.  Conrad then ran in the special election for that seat and won.