Erdős Problem #168
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Say a finite set of natural numbers is *non ternary* if it contains no 3-term arithmetic progression of the form `n, 2n, 3n`.
`IntervalNonTernarySets N` is the (fin)set of non ternary subsets of `{1,...,N}`. The advantage of defining it as below is that some proofs (e.g. that of `F 3 = 2`) become `rfl`.
`F N` is the size of the largest non ternary subset of `{1,...,N}`.
Attempts
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A reproducible floating-MIP computation extends the finite-value table for corner-free subsets of the first 3-smooth numbers from prefix 5,000 through 5,020, adding twelve OEIS A004059 rows. Two SCIP formulations agree; no proof-carrying certificate was obtained, and the density and irrationality questions remain open.
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