Brown's Criterion

A sequence 👁 {nu_i}
of nondecreasing positive integers is complete iff

1. 👁 nu_1=1
.

2. For all 👁 k=2
, 3, ...,

A corollary states that a sequence for which 👁 nu_1=1
and 👁 nu_(k+1)<=2nu_k
is complete (Honsberger 1985).

See also

Complete Sequence, Fibonacci Number, Fibonacci n-Step Number, Tribonacci Number

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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 Criterion

Cite this as:

Weisstein, Eric W. "Brown's Criterion." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BrownsCriterion.html

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