Euler's formula for the Waring number

For a positive integer $n$, let $\kappa(n)$ be the least integer $m$ such that every positive integer is a sum of $m$ nonnegative $n$th powers.

Waring-number conjecture.

$$\kappa(n)=2^n+\left\lfloor\frac{3^n}{2^n}\right\rfloor-2.$$

The formula has been computationally verified for $6\leq n<471600000$. The paper presents it as a conjecture in its concluding discussion of extensions to higher-power sequences.