Journal of Integer Sequences, Vol. 13 (2010), Article 10.1.4

Comment on "On a Generalization of the Frobenius Number"


Jeffrey Shallit
School of Computer Science
University of Waterloo
Waterloo, ON N2L 3G1
Canada

In this paper the authors ask if it is always true that g0 < g1. (To make it interesting, we need to rule out trivial cases where one number is in the N-span of the other elements.) I found many counterexamples, of which the smallest seems to be (8,9,11,14,15), with g0 = 21 and g1 = 20. (I do not know if there exists a 4-element counterexample, but I doubt it.)

Received January 11 2010.

Addendum, September 7 2010: J. Stankewicz found the 4-element counterexample (28,30,105,168) with g0 = 467 and g1 = 425. The smallest is (10, 15, 32, 48) with g0 = 101 and g1 = 99.

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