A stronger conjecture for numbers of the form $2^k 3^l 5^j$.
For any $ε > 0$, all large integers $n$ can be written as the sum of distinct integers
$b_1 < ... < b_t$ of the form $2^k 3^l 5^j$ where $b_t < (1 + ϵ) b_1$.
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theorem erdos_123.variants.powers_2_3_5_snug :
answer(sorry) ↔ ∀ ε > 0, ∀ᶠ n in atTop,
∃ A : Finset ℕ, (A : Set ℕ) ⊆ ↑(powers 2) * ↑(powers 3) * ↑(powers 5) ∧ IsSnug ε A ∧
∑ x ∈ A, x = n
