Denominators of coefficients in Stirling's expansion for $\log(\Gamma(z))$

formal-conjectures · oeis · ams-11

The $n$-th term is the denominator of $\frac{B_{2n}}{2n(2n-1)}$ where $B_{2n}$ is the $2n$-th
Bernoulli number.

Conjecture I: if $n > 2$, then $\frac{a(\text{A005382}(n))}{12}$ is prime,
where A005382 is the sequence of primes $p$ such that $2p-1$ is also prime.
- Lorenzo Sauras Altuzarra, Oct 13 2020

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/A046969
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/46969.lean
Local target: Corpus.OEIS46969.conjecture1
Source SHA-256: d4e654a673d6db9d20148408fcf36c234b77247ef1b66382582a9b8096f5ba6b
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.

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