Problem 954

../

---

Statement. Let $0=a_0<a_1<a_2<\cdots$ be the sequence of integers defined by $a_0=0$ and $a_1=1$, and $a_{k+1}$ is the smallest integer $n$ for which the number of solutions to $a_i+a_j \leq n$ (with $0\leq i\leq j\leq k$ and $j\geq 1$) is $<n$.

Is the number of solutions to $a_i+a_j \leq x$ equal to $x+O(x^{1/4+o(1)})$?

Status. Open.

Source. erdosproblems.com/954, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #954, https://www.erdosproblems.com/954.

Formalization. None recorded.

Progress

Not yet compiled.

Known Results

Not yet compiled.