bibkey: oeis2025a068012 authors: OEIS Foundation Inc.; Antti Karttunen; David A. Corneth year: 2025 title: OEIS A068012 subset sum doubling conjecture doi: null url: https://oeis.org/A068012 claim: For n greater than two with three not dividing n minus one, A068012(n) doubles. strata_touched:

• D5/S1/Recurrence/Parity/SubsetSumModSixDoubling license: citation-only triage: anchor

OEIS A068012 subset sum doubling conjecture

Directly inspected on September 8, 2026. The title is “Number of subsets of {1,2,3,…,n} that sum to 0 mod 6.” The offset is zero, and the empty subset is counted. Antti Karttunen created the entry on February 11, 2002.

David A. Corneth’s September 13, 2025 formula block explicitly states: “Conjecture: a(n) = 2*a(n-1) for n > 2 and 3 does not divide n-1.” It also reports verification through 2000. That finite calculation does not prove the universally quantified assertion.

The internal revision line at inspection was %I #28 Oct 08 2025 23:54:21. The June 2026 update mentioned in the implementation brief was not confirmed as an entry-specific revision. The page still labels the statement Conjecture.

Verified locator

• https://oeis.org/A068012
• https://oeis.org/A068012/internal: title, offset, author, and Corneth’s formula block.

Proof scope

The formal count filters the powerset of the natural interval from one to n by the sum in ZMod 6. The proof splits subsets at the last element, pairs residues differing by three, and uses the complement bijection to identify zero and one when n is one modulo three. It covers every index in the stated range. The other recurrence and closed form in the entry are not claimed here.

The implementation brief reports no independent proof in its public-index search. This worker’s GitHub code search for A068012 language:Lean returned no hits. A Google query returned a JavaScript challenge, not search results. First-publication priority and exhaustive literature coverage are not claimed.