Conjectures associated with A109845

formal-conjectures · oeis · ams-11

$a(1) = 2$; $a(2n)$ = lcm of all previous terms + 1; $a(2n+1)$ = lcm of all previous terms - 1.

Conjecture: There are infinitely many primes in this sequence.

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/A109845
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/109845.lean
Local target: Corpus.OEIS109845.conjecture
Source SHA-256: 5e5a45805e3370f6595f6ac3dc6b8cfa1d4421b52726d0b98f61d4a7dfd67296
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