The site's wording fails for $k=1,\ldots,4$: the strings $1$, $121$, $1213121$ and $121312141213121$ have length $2^k-1$ and no abelian square (the strings $121$ and $1213121$ are noted in the formal-conjectures file, and the string of length $15$ is Alexeev's, below). At length $2^k$ the question holds for $k\le3$, as Erdős reports in [Er61] (below) and as the formal-conjectures variant erdos_231.variants.two_pow_small proves for $k=2,3$ by kernel computation. It fails at $k=4$, by the site's string $1213121412132124$, which has no abelian square.

The change replaces "$2^k-1$" by "$2^k$"; nothing else changes. The evidence is Erdős's own words about instances of the question. [Er61], Part II, item 2 (Some unsolved problems, 1961), calls two consecutive blocks "identical" when each symbol occurs equally often in both, and continues: "I conjectured that in a sequence of length $2^k-1$ formed from $k$ symbols there must be two “identical” blocks. This is true for $k \leq 3$, but for $k=4$ de BRUIJN and I disproved it". Both reports are true at length $2^k$ and false at length $2^k-1$: at that length the conjecture already fails for $k\le3$, and $k=4$ is not its first failure. [Er57], item 28, printed p. 298 (Some unsolved problems, 1957), defines $N(k)$ as the least $N$ such that every sequence of length $N$ over $\{1,\ldots,k\}$ contains two adjacent blocks, each a rearrangement of the other, and reports that his "earliest conjecture, that $N(k) = 2^k - 1$, has been disproved by Bruijn and myself"; the strings above give $N(k)\ge2^k$ for $k\le3$, so this print carries the same slip. The misprint is therefore already in both of the poser's texts, and the site's wording repeats it; his words about the instances hold only for length $2^k$. The site's commentary suggests that Erdős may have meant $2^k$; that suggestion is not the evidence.

Results about the site's wording are credited here and count for nothing. Boris Alexeev gave the ruler sequence $121312141213121$ on the site's discussion thread on 2026-02-15, and the formal-conjectures statement file notes the strings $121$ and $1213121$. A Lean file in Alexeev's lean-proofs collection, whose header names de Bruijn and Erdős as informal authors and AxiomProver as formal author, published by Axiom Math, proves the negation of the site's wording, not_erdos_231, (pinned file; copy at lean-proofs) from an abelian-square-free string of length $15$ over four characters; it is linked from the de Bruijn–Erdős page and settles no instance of the corrected Statement.