Conjectures associated with A105210

formal-conjectures · oeis · ams-11

$a(1) = 393$; for $n > 1$, $a(n) = a(n-1)$ + 1 + sum of distinct prime factors of $a(n-1)$
that are $< a(n-1)$.

Cormier and Selfridge found 5 starting values for which the sequences appear to not merge.
The sequences were checked up to 10^8.

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/A105210
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/105210.lean
Local target: Corpus.OEIS105210.conjecture_disjoint_starting_values
Source SHA-256: 8b28b2d62778972789da4c5d5050374d1cdcd325278be29a6997e9defabf20e3
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