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EXAMPLE
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7 has five shortest addition chains: (1,2,3,4,7), (1,2,3,5,7), (1,2,3,6,7), (1,2,4,5,7), and (1,2,4,6,7). All of these are Brauer chains. Hence a(7) = 0.
13 has ten shortest addition chains: (1,2,3,5,8,13), (1,2,3,5,10,13), (1,2,3,6,7,13), (1,2,3,6,12,13), (1,2,4,5,9,13), (1,2,4,6,7,13), (1,2,4,6,12,13), (1,2,4,8,9,13), (1,2,4,8,12,13), and (1,2,4,5,8,13). Of these, only the last is non-Brauer. Hence a(13) = 1.
12509 has 28 shortest addition chains, all of which happen to be non-Brauer (in fact, it is the smallest natural number for which all shortest addition chains are non-Brauer). Hence a(12509) = A079300(12509) = 28.
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