erdős #168
Let be the size of the largest subset of which does not contain any set of the form . What isIs this limit irrational?
Worked, still open.
additive combinatorics · open · formalized (Lean) · 0 attempts
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vela registry pull vfr_37aec80d874a0239vela reproduce examples/erdos-problemsevidence
unverified AI candidates (2)
gpt-erdos · GPT-5.2 Pro + Deep Research · unverified
A theorem of **Graham–Spencer–Witsenhausen (1977)** shows that
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
1 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗formal
AMS 5 11 · api (literature)
lemma F_0 : F 0 = 0 := rfl
@[category API, AMS 5 11]
lemma F_1 : F 1 = 1 := rfl
@[category API, AMS 5 11]
lemma F_2 : F 2 = 2 := rfl
@[category API, AMS 5 11]
lemma F_3 : F 3 = 2 := rfl
/--
Sanity check: elements of `IntervalNonTernarySets N` are precisely non ternary subsets of
`{1,...,N}`
-/
@[category API, AMS 5 11]
lemma mem_IntervalNonTernarySets_iff (N : ℕ) (S : Finset ℕ) :
S ∈ IntervalNonTernarySets N ↔ NonTernary S ∧ S ⊆ Finset.Icc 1 Nformal-conjectures/168.lean ↗oeis
A004059 — a(n) gives position of first n in A057561.1,2,4,5,6,8,9,11,13,14,15,17,18,20,22,23,24,26,28,29,30,32,34,35,36,38,40,41,42,43,45,47,48,50,51,53,55,56,57,59,60,61,6A057561 — Size of the largest set encompassing no {x, 2x, 3x} contained in D(n) = the first n 3-smooth numbers {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, ...} (A003586).1,2,2,3,4,5,5,6,7,7,8,8,9,10,11,11,12,13,13,14,14,15,16,17,17,18,18,19,20,21,21,22,22,23,24,25,25,26,26,27,28,29,30,30,3A094708 — Size of the smallest set hitting all {x, 2x, 3x} contained in D(n) = the first n 3-smooth numbers {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27,...} (A003586).0,0,1,1,1,1,2,2,2,3,3,4,4,4,4,5,5,5,6,6,7,7,7,7,8,8,9,9,9,9,10,10,11,11,11,11,12,12,13,13,13,13,13,14,14,15,15,15,16,16,A386439 — Decimal expansion of the maximal density of a set of positive integers free of subsets of the form {n, 2n, 3n}.8,0,0,9,6,5,7,5,5,0,0,6,5,5,8,9,8,9,0,9,0,4,2,0,3,2,6,3,8,8,0,8,2,4,1
status
open