Fibonacci Dual Theorem

Let $F_n$ be the $n$th Fibonacci Number. Then the sequence $\{F_n\}_{n=2}^\infty=\{1, 2, 3, 5, 8, \dots\}$ 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.

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.