A sequence 
of nondecreasing positive
integers is complete iff
1. 
.
2. For all 
,
3, ...,
 |
A corollary states that a sequence for which 
and 
is complete
(Honsberger 1985).
Brown's Criterion
See also
Complete Sequence, Fibonacci Number, Fibonacci n-Step Number, Tribonacci NumberExplore with Wolfram|Alpha
References
Brown, J. L. Jr. "Notes on Complete Sequences of Integers." Amer. Math. Monthly 68, 557-560, 1961.Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., pp. 123-130, 1985.Referenced on Wolfram|Alpha
Brown's CriterionCite this as:
Weisstein, Eric W. "Brown's Criterion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BrownsCriterion.html