Efficient Algorithms for Zeckendorf Arithmetic
  We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be performed by combinational logic networks with linear size and logarithmic depth. The implications of these results for multiplication, division and square-root extraction are also discussed. 
Connor Ahlbach, Jeremy Usatine and Nicholas Pippenger
cs.DS math.CO