Erdős Problem 840

### What is the conjecture

https://www.erdosproblems.com/840

Let $f(N)$ be the size of the largest quasi-Sidon subset $A\subset\\{1,\ldots,N\\}$, where we say that $A$ is quasi-Sidon if
$$\lvert A+A\rvert=(1+o(1))\binom{\lvert A\rvert}{2}.$$
How does $f(N)$ grow?

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

Read the linked Erdős Problem 840 statement and compare existing formal-conjecture entries in the repository to determine the expected Lean structure. Done means the conjecture is added as a compiling formal statement; no target file or test is named in this issue.

Written by the indexing model from the issue text.