Zeckendorf's Theorem

The Sequence $\{F_n-1\}$ is Complete even if restricted to subsequences which contain no two consecutive terms, where $F_n$ is a Fibonacci Number.

See also Fibonacci Dual Theorem, Zeckendorf Representation

References

Brown, J. L. Jr. ``Zeckendorf's Theorem and Some Applications.'' Fib. Quart. 2, 163-168, 1964.

Keller, T. J. ``Generalizations of Zeckendorf's Theorem.'' Fib. Quart. 10, 95-112, 1972.

Lekkerkerker, C. G. ``Voorstelling van natuurlijke getallen door een som van Fibonacci.'' Simon Stevin 29, 190-195, 1951-52.