Recurrence involving LCM: $a(n) = x(n+1)/x(n) - 2$

formal-conjectures · oeis · ams-11

$a(n) = x(n+1)/x(n) - 2$ where $x(1)=1$ and $x(n) = 2 x(n-1) + \operatorname{lcm}(x(n-1),n)$
for $n > 1$.

Conjecture: For prime $p$ such that $p-2$ is not a prime, $a(p-1) = p$.
- _Bill McEachen_, Sep 26 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/A135508
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/135508.lean
Local target: Corpus.OEIS135508.conjecture
Source SHA-256: d30e39ccec3b32a89e48ed0ef1fe2be939a526a2ccae61ce4998ce5741ccfefd
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