Rowland-style prime-generating recurrence

formal-conjectures · oeis · ams-11

The sequence is defined by $a(1) = 2$ and for $n \ge 2$:
$a(n) = a(n-1) + \gcd(n, a(n-1))$ if $n$ is even, and
$a(n) = a(n-1) + \gcd(n-2, a(n-1))$ if $n$ is odd.

Conjecture: Every record of differences $a(n)-a(n-1)$ more than 5 is the greater of twin primes
(A006512).

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/A166944
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://arxiv.org/abs/0910.4676
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/166944.lean
Local target: Corpus.OEIS166944.conjecture
Source SHA-256: ad9a7a93b957f94f199db56f9281d90b7eb9a21a0c4b3412bc816d8098ea8b7a
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