Let 
be the 
th
Fibonacci number. Then the sequence 
is complete,
even if one is restricted to subsequences in which no two consecutive terms are both
passed over (until the desired total is reached; Brown 1965, Honsberger 1985).
Fibonacci Dual Theorem
See also
Complete Sequence, Fibonacci NumberExplore with Wolfram|Alpha
References
Brown, J. L. Jr. "A New Characterization of the Fibonacci Numbers." Fib. Quart. 3, 1-8, 1965.Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., p. 130, 1985.Referenced on Wolfram|Alpha
Fibonacci Dual TheoremCite this as:
Weisstein, Eric W. "Fibonacci Dual Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FibonacciDualTheorem.html