bibkey: hanna2026a397348 authors: Paul D. Hanna year: 2026 title: “OEIS A397348: exponential square-weight congruence” doi: null url: https://oeis.org/A397348 claim: “Conjecture: a(n) is odd iff n+1 is a power of 2.” strata_touched:

• D5/S1/Recurrence/Residue/ParametricExponentialSquareCongruence license: citation-only triage: anchor

OEIS A397348

NAME: O.g.f. satisfies A(x) = exp(x + Sum_{n>=2} (3*n^2-1)*a(n)x^n/(3n^2)).

Conjecture: a(n) is odd iff n+1 is a power of 2.

The continuation worker retrieved the full OEIS JSON (revision 10) on 2026-09-09 and read the NAME, COMMENT, FORMULA, REFERENCE, LINK and XREF fields. No target proof is linked there or in the directly referenced entries read in this attempt. This is a bounded literature check, not a priority claim. The unrelated formula (6) conflicts with the companion entry’s inverse formula and is not used. Formal source correspondence uses the NAME itself.

The proof, per-declaration audit, reverified predecessor contributions and limitations are recorded in Library/Recurrence/hanna2026a397family.md. The formal theorem parity_q3 uses the new generic source_iff correspondence. No asymptotic limit is asserted.

Verified locator

• URL: https://oeis.org/A397348