Piatetski-Shapiro sequences N_(c) contain thin subbases A of order h>=5 (for 1<c<2) or h>=(floor(2c)+1)(floor(2c)+2)+1 (for c>2), with r_{A,h}(n) ~ F(n) for regularly varying F satisfying the stated growth bounds.
Madritsch,Waring’s problem for pseudo-polynomials
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Thin subbases of Piatetski-Shapiro sequences
Piatetski-Shapiro sequences N_(c) contain thin subbases A of order h>=5 (for 1<c<2) or h>=(floor(2c)+1)(floor(2c)+2)+1 (for c>2), with r_{A,h}(n) ~ F(n) for regularly varying F satisfying the stated growth bounds.