Collatz step differences

formal-conjectures · oeis · ams-11

Differences in adjacent elements of the sequence quantifying the steps needed for $n$ to
converge to 1 in the Collatz Conjecture.
$$a(n) = \mathrm{A006577}(n+1) - \mathrm{A006577}(n)$$
for $n > 0$.

Conjecture 1: More than half of the terms are 0.
- _Ya-Ping Lu_, May 04 2024

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/A153330
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/153330.lean
Local target: Corpus.OEIS153330.conjecture1
Source SHA-256: 805cb93a4356ec755a413022e91b59042ee59d23eec1852f1423b885b671d12b
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