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Least positive multiple of $n$ in base 10 with digits 0 and 1: conjecture

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Statement

It is known that a(10k−1)=(109k−1)/9a(10^k - 1) = (10^{9k} - 1) / 9 for all kk. Is a(n)<a(10k−1)a(n) < a(10^k - 1) for all n<10k−1n < 10^k - 1?

  • David Radcliffe, Aug 01 2025

Lean statement

theorem conjecture (k : ℕ) :
    ∀ n < 10 ^ k - 1, a n < a (10 ^ k - 1) := by
  sorry

Sources(1)

Openness evidence

Tagged category research open in google-deepmind/formal-conjectures at commit a64e959c32c2. Definitions used by the statement are in FormalConjectures/OEIS/4290.lean.

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