Juggler conjecture

formal-conjectures · wikipedia · ams-11 · ams-37

Now form a sequence beginning with any positive integer, where each subsequent term is obtained
by applying the operation defined above to the previous term.
The **Juggler Conjecture** states that for any positive integer $n$, there exists a natural number
$m$ such that the $m$-th term of the sequence is $1$.

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://en.wikipedia.org/wiki/Juggler_sequence
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/JugglerConjecture.lean
Local target: Corpus.WikipediaJugglerConjecture.juggler_conjecture
Source SHA-256: 7272b0fcd00297994b897753fdcb9ea4b15e9e2536d8f4828578519b398aabfd
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