Journal of Integer Sequences, Vol. 18 (2015), Article 15.10.5

Generalized Anti-Waring Numbers

Chris Fuller and Robert H. Nichols, Jr.
Labry School of Science, Technology, and Business
Cumberland University
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.

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(Concerned with sequence A001661.)

Received June 18 2015; revised version received September 13 2015; September 21 2015. Published in Journal of Integer Sequences, September 24 2015.

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