Geodesic
Generalized anti-Waring numbers
Journal of integer sequences, Tome 18 (2015) no. 10
The anti-Waring problem considers the smallest positive integer such that it and every subsequent integer can be expressed as the sum of the $k^{th}$ 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.
Classification : 11P05, 05A17
Keywords: complete sequence, sum of powers, anti-Waring number 
@article{JIS_2015__18_10_a5,
     author = {Fuller,  Chris and Nichols,  Robert H.jun.},
     title = {Generalized {anti-Waring} numbers},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {10},
     zbl = {1334.11079},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a5/}
}
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Fuller,  Chris; Nichols,  Robert H.jun. Generalized anti-Waring numbers. Journal of integer sequences, Tome 18 (2015) no. 10. http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a5/