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Phi Number System

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


where $\phi$ is the Golden Mean.


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.

© 1996-9 Eric W. Weisstein