From http://wwwhomes.uni-bielefeld.de/achim/addition_chain.html :
In August 2005 Neill Clift reported to have confirmed the Scholz-Brauer inequality for all n<5784689 = 222+97*214+65*24+97. This number is also the smallest Non-Hansen number (also identified by Neill Clift in 2005 as such).
As far as I know, it is still an outstanding conjecture that there is always a minimal addition chain for n that is a Hansen chain.
Franklin T. Adams-Watters
Apparently not any more. According to http://wwwhomes.uni-bielefeld.de/achim/addition_chain.html : In August 2005 Neill Clift reported to have confirmed the Scholz-Brauer inequality for all n<5784689 = 222+97*214+65*24+97. This number is also the smallest Non-Hansen number (also identified by Neill Clift in 2005 as such).