The golden ratio $\phi=\frac{1+\sqrt{5}}{2}=1/61803398874...$ is the root of the polynomial $x^2-x-1=0$, and is the one of the important numbers in mathematics. The golden ratio is also used in many fields of science. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts. In this paper, we present a sequence of golden numbers $\{\phi_n\}_n$ and study their properties.
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