Let $A \subseteq {1, \dots N}$ be a set such that there exists at most one $n$ with more than one solution to $n = a + b$ (with $a \leq b \in A$ ). Estimate the maximal possible size of $∣ A ∣$ - in particular, is it true that $∣ A ∣ \leq (1 + o (1)) \frac{2}{3} N^{1/2} ?$

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number theory · open · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

[ r^*(n):=|\\{(a,b)\in A^2:\ a\le b,\ a+b=n\\}|. ]

candidate solution ↗

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

candidate solution ↗

oeis

A389182 — Maximum cardinality of a subset of {1,...,n} in which all sums a+b of elements a<=b are distinct except possibly one.1,2,3,3,4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,12,12,

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Vela Sidon frontier (A309370) · verified work

A B₂/Sidon problem — the same object family as Vela's verified Sidon records, where nine improved terms were accepted into OEIS A309370 (the campaign's first external adoption).

OEIS A309370 ↗ · verified-combinatorics (witnesses + verify.py) ↗ · the Erdős campaign

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