Weakly Complete Sequence
المؤلف:
Graham, R.
المصدر:
"A Property of Fibonacci Numbers." Fib. Quart. 2
الجزء والصفحة:
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8-11-2020
906
Weakly Complete Sequence
A sequence of numbers
{nu_n}" src="https://mathworld.wolfram.com/images/equations/WeaklyCompleteSequence/Inline1.gif" style="height:15px; width:50px" /> 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.
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