An algorithm for computing an Egyptian fraction, called the Farey sequence method by Bleicher (1972).
Bleicher, M. N. "A New Algorithm for the Expansion of Continued Fractions." J. Number Th. 4, 342-382, 1972.
Eppstein, D. Egypt.ma Mathematica notebook. http://www.ics.uci.edu/~eppstein/numth/egypt/egypt.ma.