A sequence of numbers V = {ν_n} is complete if every positive integer n is the sum of some subsequence of V, i.e., there exist a_i = 0 or 1 such that n = sum_(i = 1)^∞ a_i ν_i (Honsberger 1985, pp. 123-126). The Fibonacci numbers are complete. In fact, dropping one number still leaves a complete sequence, although dropping two numbers does not. The sequence of primes with the element {1} prepended, {1, 2, 3, 5, 7, 11, 13, 17, 19, 23, ...} is complete, even if any number of primes each >7 are dropped, as long as the dropped terms do not include two consecutive primes. This is a consequence of Bertrand's postulate.

Bertrand's postulate | Brown's criterion | Fibonacci dual theorem | greedy algorithm | weakly complete sequence | Zeckendorf's theorem