Recurrence $a(n) = (a(n-1) + a(n-2)) \pmod n$

formal-conjectures · oeis · ams-11

$a(0) = a(1) = 1$; $a(n) = (a(n-1) + a(n-2)) \pmod n$.

All numbers appear infinitely often, i.e., for every number $k \ge 0$ and every frequency $f > 0$
there is an index $i$ such that $a(i) = k$ is the $f$-th occurrence of $k$ in the sequence.
- _Klaus Brockhaus_, Aug 29 2006

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/A096535
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/96535.lean
Local target: Corpus.OEIS96535.conjecture
Source SHA-256: 0e819dea8846a0bc4129ac78af9af2b86b6f966ef57e2a31e8379e3caa90c40b
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