Complete Sequence
A Sequence of numbers 
is complete if every Positive Integer 
is the sum of somesubsequence of 
, i.e., there exist 
or 1 such that
(Honsberger 1985, pp. 123-126). The Fibonacci Numbers are complete. In fact, dropping onenumber still leaves a complete sequence, although dropping two numbers does not (Honsberger 1985, pp. 123 and 126). TheSequence of Primes with the element
prepended,
is complete, even if any number of Primes each
are dropped, as long as the dropped terms do not include twoconsecutive Primes (Honsberger 1985, pp. 127-128). This is a consequence of Bertrand's Postulate.See also Bertrand's Postulate, Brown's Criterion, Fibonacci Dual Theorem, Greedy Algorithm,Weakly Complete Sequence, Zeckendorf's Theorem
References
Brown, J. L. Jr. ``Unique Representations of Integers as Sums of Distinct Lucas Numbers.'' Fib. Quart. 7, 243-252, 1969. Hoggatt, V. E. Jr.; Cox, N.; and Bicknell, M. ``A Primer for Fibonacci Numbers. XII.'' Fib. Quart. 11, 317-331, 1973. Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., 1985.
- Golden Rule
- Golden Section
- Golden Theorem
- Golden Triangle
- Goldschmidt Solution
- Golomb Constant
- Golomb-Dickman Constant
- Golomb Ruler
- Golygon
- Gomory's Theorem
- Gompertz Constant
- Gompertz Curve
- Gonal Number
- Goodman's Formula
- Good Path
- Good Prime
- Goodstein Sequence
- Goodstein's Theorem
- Googol
- Googolplex
- Gordon Function
- Gorenstein Ring
- Gosper Island
- Gosper's Algorithm
- Gosper's Method