Half-Fibonacci sequence

formal-conjectures · oeis · ams-11

$a(0) = 1, a(1) = 3$; for $n \ge 2$, $a(n) = f(a(n-1)) + f(a(n-2))$ where $f(x) = x/2$ if $x$
is even
and $f(x) = x$ if $x$ is odd.

Conjecture (1): The natural density of even terms in the sequence is $1/2$.

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/A120424
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/120424.lean
Local target: Corpus.OEIS120424.conjecture1
Source SHA-256: c803ea7cfea0fda22ed7e9383a4e809b337a5e03481bbee839d4bd8385943c81
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