
EXAMPLE

All five of the shortest addition chains for 7 are Brauer chains: (1,2,3,4,7), (1,2,3,5,7), (1,2,3,6,7), (1,2,4,5,7), (1,2,4,6,7). Hence a(7) = 5.
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, all but the last are Brauer chains. Hence a(13) = 9.
12509 has 28 shortest addition chains, none of which are Brauer chains. Hence a(12509) = 0.
