Phi Number System

For every Positive Integer $n$, there is a corresponding finite sequence of distinct Integers $k_1$, ..., $k_m$ such that

$$n=\phi^{k_1}+\ldots+\phi^{k_m},$$

where $\phi$ is the Golden Mean.

References

Bergman, G. ``A Number System with an Irrational Base.'' Math. Mag. 31, 98-110, 1957.

Knuth, D. The Art of Computer Programming, Vol. 1: Fundamental Algorithms, 2nd ed. Reading, MA: Addison-Wesley, 1973.

Rousseau, C. ``The Phi Number System Revisited.'' Math. Mag. 68, 283-284, 1995.