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


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

See also

Complete Sequence

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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.

Referenced on Wolfram|Alpha

Weakly Complete Sequence

Cite this as:

Weisstein, Eric W. "Weakly Complete Sequence." From MathWorld--A Wolfram Web Resource.

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