Weakly Complete Sequence

A sequence of numbers  is said to be weakly complete if every positive integer  beyond a certain point  is the sum of some subsequence of  (Honsberger 1985). Dropping two terms from the Fibonacci numbers produces a sequence which is not even weakly complete. However, the sequence

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

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.