Fibonacci Dual Theorem

Let F_n be the nth Fibonacci number. Then the sequence {F_n}_(n=2)^infty={1,2,3,5,8,...} 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).

See also

Complete Sequence, Fibonacci Number

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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 Theorem

Cite this as:

Weisstein, Eric W. "Fibonacci Dual Theorem." From MathWorld--A Wolfram Web Resource.

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