Smallest factorial containing exactly $n$ 6's

formal-conjectures · oeis · ams-11

The sequence $a(n)$ gives the smallest $k$ such that the decimal expansion of $k!$
contains exactly $n$ occurrences of the digit '6', or $0$ if no such $k$ exists.

It is conjectured that $a(24) = 0$ since no factorial less than $10000$ contained just 24 sixes.

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/A072200
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/72200.lean
Local target: Corpus.OEIS72200.conjecture
Source SHA-256: 4df61004dd19c0d785b777467ec9fe0d0e9b1b7450639a49f236c9df21d9f27e
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