Hint: Use again the window-method on the binary representation *101100110000110011000001011110*_{2} of the value *2n*. The simple trick is to find an optimal addition chain for *179=10110011*_{2} which contains *51=110011*_{2} and *94=1011110*_{2}.
Then one can easily construct a star chain of length 34 by hand for *2n*.