Geodesic
An elementary proof that any natural number can be written as the sum of three terms of the sequence $\lfloor \frac{n}{2/3} \rfloor $
Journal of integer sequences, Tome 17 (2014) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We give an elementary proof that any natural number can be written as the sum of three terms of the sequence $\lfloor n^{2}/3 \rfloor _{n \in N}$ . This is a recent conjecture of the author that was very recently confirmed by Mezroui et al.; they used a result due to Bateman and derived from the theory of modular forms. We also state some conjectures related to the subject.
Keywords: sum of squares, Legendre's theorem, additive bases 
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     author = {Farhi, Bakir},
     title = {An elementary proof that any natural number can be written as the sum of three terms of the sequence $\lfloor \frac{n}{2/3} \rfloor $},
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Farhi, Bakir. An elementary proof that any natural number can be written as the sum of three terms of the sequence $\lfloor \frac{n}{2/3} \rfloor $. Journal of integer sequences, Tome 17 (2014) no. 7. http://geodesic.mathdoc.fr/item/JIS_2014__17_7_a1/