$a(n) = \sum_{k=1}^n (k^2 \bmod n)$

formal-conjectures · oeis · ams-11

"Conjecture: $a(n) <= \frac{n^2-1}{2}$. - _Aspen A.M. Meissner_, Mar 06 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/A048153
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/48153.lean
Local target: Corpus.OEIS48153.conjecture
Source SHA-256: e1e3507af18276913ff03726fd452eb50032976dc7785f2fa31dcecd65b09b09
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