The sequence 
is complete even
if restricted to subsequences which contain no two consecutive terms, where 
is a Fibonacci
number.
Zeckendorf's Theorem
See also
Fibonacci Dual Theorem, Zeckendorf RepresentationExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Zeckendorf's TheoremCite this as:
Weisstein, Eric W. "Zeckendorf's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ZeckendorfsTheorem.html