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A Brauer chain is an Addition Chain in which each member uses the previous member as a summand. A number 
for which a shortest chain exists which is a Brauer chain is called a Brauer Number.
See also Addition Chain, Brauer Number, Hansen Chain
References
Guy, R. K. ``Addition Chains. Brauer Chains. Hansen Chains.'' §C6 in
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 111-113, 1994.