Generalized Anti-Waring Numbers
Chris Fuller and Robert H. Nichols, Jr.
Labry School of Science, Technology, and Business
1 Cumberland Square
Lebanon, TN 37087
The anti-Waring problem considers the smallest positive integer such
that it and every subsequent integer can be expressed as the sum of the
kth powers of r
or more distinct natural numbers. We give a
generalization that allows elements from any nondecreasing sequence,
rather than only the natural numbers. This generalization is an
extension of the anti-Waring problem, as well as the idea of complete
sequences. We present new anti-Waring and generalized anti-Waring
numbers, as well as a result to verify computationally when a
generalized anti-Waring number has been found.
Full version: pdf,
(Concerned with sequence
Received June 18 2015; revised version received September 13 2015;
September 21 2015.
Published in Journal of Integer Sequences, September 24 2015.
Journal of Integer Sequences home page