Erdős problem 357

Let $f(n)$ be the maximal $k$ such that there exist integers $1 \le a_1 < \dotsc < a_k \le n$ such that all sums of the shape $\sum_{u \le i \le v} a_i$ are distinct. It is known that $f(n) \geq (2+o(1))\sqrt{n}$ . Source: See comment by Desmond Weisenberg here: https://www.erdosproblems.com/forum/thread/357.

Sources

The source's own material, retained exactly.

17 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

357.lean

Retained formal statement17 of 17

Let $f(n)$ be the maximal $k$ such that there exist integers $1 \le a_1 < \dotsc < a_k \le n$ such that all sums of the shape $\sum_{u \le i \le v} a_i$ are distinct. It is known that $f(n) \geq (2+o(1))\sqrt{n}$ . Source: See comment by Desmond Weisenberg here: https://www.erdosproblems.com/forum/thread/357.

FormalConjectures/ErdosProblems/357.leanErdos357.erdos_357.variants.weisenberg1 lineExact file

1∃ o, o =o[Filter.atTop] 1 ∧ ∀ᶠ (n : ℕ) in Filter.atTop, (2 + o n) * √↑n ≤ ↑(Erdos357.f n)

SolvedStatement only, no proof