Erdős problem 357 · problems.science

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

Browse retained paths and inspect the exact material available for this Problem.

17 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

357.lean

Retained formal statement4 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. How does $f(n)$ grow? Can we find a (good) explicit function $g$ such that $f = \Theta(g)$ ?

FormalConjectures/ErdosProblems/357.leanErdos357.erdos_357.parts.ii.bigTheta_version1 lineExact file

1(fun n => ↑(Erdos357.f n)) =Θ[Filter.atTop] sorry

OpenStatement only, no proof

Sources

Search problems.science