Difference of digit sums in base 3 and base 2

formal-conjectures · oeis · ams-11

Difference of sums of digits of $n$ in ternary and in binary:
$$a(n) = \sum \mathrm{digits}_3(n) - \sum \mathrm{digits}_2(n).$$

"This sequence is positive on average, since 1/log(3) > 1/log(4). Do all integers appear
infinitely often?" - Charles R Greathouse IV, Feb 07 2013

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/A180017
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/180017.lean
Local target: Corpus.OEIS180017.conjecture
Source SHA-256: 850c72ab23bae63878401363f01ac5c14a7b45db52996d3e1fbb72d221336fb5
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