Trajectory of 103 under the Reverse and Add! operation in base 3

formal-conjectures · oeis · ams-11

The sequence $a(n)$ is the trajectory of $103$ under the Reverse and Add! operation carried out
in base $3$, written in base $10$.
$a(0) = 103$, and $a(n+1) = a(n) + \text{rev}_3(a(n))$.

$103$ is conjectured to be the smallest number such that the Reverse and Add! algorithm in base $3$
does not lead to a palindrome. Its trajectory is conjectured to never reach a palindrome.

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/A077408
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/77408.lean
Local target: Corpus.OEIS77408.conjecture
Source SHA-256: de2f1f8d077e31006f5938978606e17ea083e76c4220e718620e2b8b8ede350b
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.

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