Fibonacci Dual Theorem
Let 
be the 
th Fibonacci Number. Then the sequence 
isComplete, even if one is restricted to subsequences in which no two consecutive terms are bothpassed over (until the desired total is reached; Brown 1965, Honsberger 1985).
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.
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