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bibkey: hanna2018a300732 authors: Paul D. Hanna year: 2018 title: “OEIS A300732: vanishing-diagonal index divisibility” doi: null url: https://oeis.org/A300732 claim: “G.f. A(x) satisfies: [x^n] A( x/A(x)^(2*n) ) = 0 for n>=1. Conjecture: n divides a(n) for n>=1.” strata_touched:

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

A300732: vanishing-diagonal index divisibility

Quoted directly from this entry’s seat-local oeis-A300732.src (seats/opB-diagidx2/oeis-A300732.src in the supplied workspace):

NAME: G.f. A(x) satisfies: [x^n] A( x/A(x)^(2*n) ) = 0 for n>=1. COMMENT: Conjecture: n divides a(n) for n>=1. AUTHOR: Paul D. Hanna, Mar 11 2018

The printed NAME imposes vanishing for n>=1. The entry’s own DATA begins with 1,1, so the substituted coefficient in degree one is one. The formal instance corrects the vanishing range to n>1 and retains a(0)=a(1)=1. This is an editorial interpretation of the source, not a proof of its literal degree-one condition; external identification remains ASSUMED-UNVERIFIED.

The named theorem is hanna_conjecture_a300732 in D5/S1/Recurrence/Residue/DiagonalVanishingIndexDivisibility.lean. The entry-specific resolution dossier is Problems/oeis-a300732-diagonal-index-divisibility.md.

ASSUMED-UNVERIFIED: the local source was read without network access; live OEIS text, revision history and publication priority were not checked here.

Verified locator

  • URL: https://oeis.org/A300732