Imaginary part of $\prod_{k=0}^n (1 + k \cdot i)$, $i = \sqrt{-1}$

formal-conjectures · oeis · ams-11

Moll's conjecture 5.5 extends to this sequence and takes the form:
(ii) for the other primes of type $2$, the p-adic valuation
$\nu_p(a(n)) \sim n/(p - 1)$ as $n \rightarrow \infty$.

(Type 2 primes consists of primes p == 1 (mod 4))

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/A105751
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/105751.lean
Local target: Corpus.OEIS105751.conjecture.variants.moll_p_mod_4_eq_1
Source SHA-256: 58230779dbf59230c2e7e9dfd20914aa3474abfc1f61093317590d377d221001
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