bibkey: hanna2026a392525
authors: Paul D. Hanna
year: 2026
title: OEIS A392525, g.f. satisfying A(x)^3 = A(x^3 + 15*x*A(x)^3)
doi: null
url: https://oeis.org/A392525
claim: 'G.f. satisfies: A(x) = A( x^3 + 15*x*A(x)^3 )^(1/3), with A(0)=0, A''(0)=1. (1) A(x)^3 = A( x^3 + 15*x*A(x)^3 ). Conjecture: a(n) is odd iff n = 2^k for k >= 0.'
strata_touched:
  - D5/S1/Recurrence/Invariants/CubicFifteenSubstitutionParity
license: citation-only
triage: anchor

OEIS A392525

Paul D. Hanna’s entry defines the generating function by the displayed cubic functional equation, with constant coefficient zero and linear coefficient one, and states the parity conjecture quoted above. Formula (1) is the defining equation used in the formalization. With the stated normalization it is the cubed form of the NAME; the cube-root operation itself is not formalized. The separate conjecture about residues modulo ten is not asserted here.

Verified locator

• URL: https://oeis.org/A392525