Weakly Complete Sequence

A Sequence of numbers $V=\{\nu_n\}$ is said to be weakly complete if every Positive Integer $n$ beyond a certain point $N$ is the sum of some Subsequence of $V$ (Honsberger 1985). Dropping two terms from the Fibonacci Numbers produces a Sequence which is not even weakly complete. However, the Sequence

$$F_n'\equiv F_n-(-1)^n$$

is weakly complete, even with any finite subsequence deleted (Graham 1964).

See also Complete Sequence

References

Graham, R. ``A Property of Fibonacci Numbers.'' Fib. Quart. 2, 1-10, 1964.

Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., p. 128, 1985.