Array read by upward antidiagonals

formal-conjectures · oeis · ams-11

Array read by upward antidiagonals: row $n$ ($n \ge 0$) contains the numbers
$m^2 - n^2$, $m \ge n+1$.

A "Goldbach Conjecture" for this sequence: when there are $n$ terms between consecutive odd
integers $2n+1$ and $2n+3$ for $n > 0$, at least one will be the product of 2 primes
(not necessarily distinct). Example: $n=3$ for consecutive odd integers $a(7) = 7$ and
$a(11) = 9$ and of the 3 sequence entries $a(8) = 12$, $a(9) = 15$ and $a(10) = 16$ between
them, one is the product of 2 primes $a(9) = 15=3*5$. - _Michael Hiebl_, Jul 15 2007

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/A105020
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/105020.lean
Local target: Corpus.OEIS105020.conjecture
Source SHA-256: 19d11eb1923e70aacbf7697a914cd3a78ce30bd897c9d2e9b5d2854bdd30f2d4
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