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 alsoComplete Sequence, Fibonacci Number
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ReferencesBrown, 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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Cite this as:
Weisstein, Eric W. "Fibonacci Dual Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FibonacciDualTheorem.html