A published paper or arXiv preprint answers the main question of Erdős Problem #341 (theorem erdos_341 in formal-conjectures) in full (proof, disproof, or the exact value asked for) with no hypotheses beyond the problem's own.

The problem, as stated in formal-conjectures (Apache 2.0):

Let A=\{a_1 < \cdots < a_k\} be a finite set of integers and extend it to an infinite sequence \overline{A}=\{a_1 < a_2 < \cdots \} by defining a_{n+1} for n \geq k to be the least integer exceeding a_n which is not of the form a_i + a_j with i,j \leq n. Is it true that the sequence of differences a_{m+1}-a_m is eventually periodic? This problem is discussed under Problem 7 on Green's open problems list. The answer is no: Li [Li26] (with GPT-5.6 Sol) showed that the greedy extension of the seed set A = \{1, 2, 3, 5, 7, 13, 22, 27, 28, 32, 36, 40, 47, 48, 52, 63, 71, 77, 81, 89, 97\} has a sequence of differences that is not eventually periodic. The linked formal proof exhibits such a sequence `a : ℕ → ℕ` (strictly increasing, with the greedy rule holding from some index on, and with `n ↦ a (n + 1) - a n` not eventually periodic); casting it to `ℤ` gives a counterexample to the statement below.