bibkey: hanna2026a396797
authors: Paul D. Hanna
year: 2026
title: OEIS A396797, G.f. satisfies A(x) = x + A^3(x)*A^4(x)
doi: null
url: https://oeis.org/A396797
claim: "G.f. satisfies A(x) = x + A^3(x)*A^4(x). Conjecture: a(n) = 1 (mod 6) for n >= 1."
strata_touched:
  - D5/S1/Recurrence/Invariants/ThreeFourIterateProductModSix
license: citation-only
triage: anchor

OEIS A396797

Paul D. Hanna’s entry, dated June 15, 2026, defines the generating series by A(x) = x + A^3(x)*A^4(x), where the superscripts denote compositional iteration. Its first conjecture states: “a(n) = 1 (mod 6) for n >= 1.” The Lean module constructs the unique zero-constant integer series satisfying this equation and proves the conjectured congruence for every positive index.

Verified locator

• URL: https://oeis.org/A396797