On the rational approximations to the real numbers corresponding to the   differences of the Fibonacci sequence
  Based on the structure of Fibonacci sequence, we give a new proof for the irrationality exponents of the Fibonacci real numbers. Moreover, we obtain all the irrationality exponents of the real numbers corresponding to the differences of Fibonacci sequence. 
Ying-jun Guo, Zhi-xiong Wen and Jie-meng Zhang
math.NT