Can we find $\alpha>1$ such that $u=(\lfloor n^\alpha\rfloor)\_{n\geqslant0}$ is an additive basis of order $2$ (i.e. $\forall x\in\mathbb{N}, \exists(n,m)\in\mathbb{N}^2, x=u\_n+u\_m$) ?


**Remark** : This question has been [asked previously on math.SE](https://math.stackexchange.com/questions/2838191/additive-basis-of-order-2), but no response has been provided yet.



Additive basis of order 2
For $1<\alpha<\frac32$, $(\lfloor n^{\alpha}\rfloor)\_{n\geqslant0}$ is an asymptotic basis of order 2. I finally found these two articles:


J-M. Deshouillers, [**Un problème binaire en théorie additive**](http://matwbn.icm.edu.pl/ksiazki/aa/aa25/aa2549.pdf), Acta Arith. 25 (1974), 393-403


S.V. Konyagin, [**An additive problem with fractional powers**](http://cds.cern.ch/record/720991/files/sis-2004-086.ps), Mathematical Notes, 2003, 73:4, 594–597


