Number of times $n$ occurs as a binary sub-pattern of $n^2$

formal-conjectures · oeis · ams-11

The sequence $a(n)$ is the number of times the binary expansion of $n$ appears as a contiguous
sublist (infix) in the binary expansion of $n^2$.

Is $a(n) \le 1$ for all $n$?

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/A076141
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/76141.lean
Local target: Corpus.OEIS76141.conjecture
Source SHA-256: f77b3ad3727aa32b06917b1cc0b701c604659058f17ab950620fd56661812c2c
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