Smallest power with base>1 and exponent $n$ without digit 0

formal-conjectures · oeis · ams-11

For statistical reasons it is conjectured that the sequence is finite.
Also it is conjectured that $a(40)$ does not exist (i.e. the sequence is empty for $n=40$).

For statistical reasons it is conjectured that the sequence is finite.
This is formalized as the assertion that for large enough $n$, no valid zeroless power exists,
which in our definition results in $a(n) = 0$.

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/A103662
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/103662.lean
Local target: Corpus.OEIS103662.conjecture
Source SHA-256: 7659d639bbd603c5db4c63ec64415e64f81234814a4b530b17d4f345ad3c204d
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