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

formal-conjectures · oeis · ams-11

Least positive multiple of $n$ that when written in base 10 uses only 0's and 1's.

It is known that $a(10^k - 1) = (10^{9k} - 1) / 9$ for all $k$.
Is $a(n) < a(10^k - 1)$ for all $n < 10^k - 1$?
- David Radcliffe, Aug 01 2025

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A004290
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/4290.lean
Local target: Corpus.OEIS4290.conjecture
Source SHA-256: 66f6a1317d050f36cd2e169ee9ad0f30095399edc41468ff4b8f84d8a8fe17b1
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record