Erdős Problem 345

### What is the conjecture

https://www.erdosproblems.com/345

Let $A\subseteq \mathbb{N}$ be a complete sequence, and define the threshold of completeness $T(A)$ to be the least integer $m$ such that all $n\geq m$ are in
$P(A) = \\{\sum_{n\in B}n : B\subseteq A\textrm{ finite }\\}$
(the existence of $T(A)$ is guaranteed by completeness). Is it true that there are infinitely many $k$ such that $T(n^k)>T(n^{k+1})$?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else