The numbers 0, 1, 2, 4, 5, 8, 9, and 10 form the first eight elements (i.e., elements a_0 to a_7) of the Fibbinary sequence. The name is a portmanteau that arose because of connections to Fibonacci numbers and binary numbers. The connection to Fibonacci numbers F(k)is that if the Zeckendorf expansion of n is
n = F(k_1) + F(k_2) + \ldots + F(k_m),
then
a_n = 2^{k_1-2}+2^{k_2-2}+\ldots+2^{k_m-2}
The connection to binary numbers is that the binary representations of the Fibbinary numbers have no adjacent 1s.
For example, = 10. The Zeckendorf expansion of 7 is 2+5, or F(3)+F(5), and
10=2^{3-2}+2^{5-2} = 2+8
Also, the binary expansion of 10 is 1010, which has no adjacent 1s.
Write a function to find the nth Fibbinary number.
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