bibkey: hanna2026a396807
authors: Paul D. Hanna
year: 2026
title: OEIS A396807, G.f. satisfies A(x) = x + A^5(x)*A^6(x)
doi: null
url: https://oeis.org/A396807
claim: "Conjecture: a(n) = 1 (mod 10) for n >= 1."
strata_touched:
  - D5/S1/Recurrence/Invariants/CompositionalIterateCongruence
license: citation-only
triage: anchor

OEIS A396807

Paul D. Hanna’s entry, dated June 16, 2026, defines the generating series by A(x) = x + A^5(x)*A^6(x), where the superscripts denote compositional iteration, not ordinary powers. It records the quoted coefficient congruence as a conjecture. The Lean module constructs the integer coefficient sequence, proves its generating equation and uniqueness, and proves the congruence for every positive index. The proof is derived in this repository.

Verified locator

• URL: https://oeis.org/A396807