Proof of the Modulo 4 Conjecture for OEIS A141117 and of the Parity Conjecture for OEIS A091713

Q: What does this research mean for the field?

Every coefficient of the generating function for OEIS A091713 is odd, and for n > 1, the coefficient a(n) for OEIS A141117 is divisible by 4 exactly when 3 divides n, and is congruent to 2 modulo 4 otherwise. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Yuan Chi

doi:10.5281/zenodo.22026845

August 20, 2026Open Access

Proof of the Modulo 4 Conjecture for OEIS A141117 and of the Parity Conjecture for OEIS A091713

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Key Points

To establish rigorous proofs for the parity conjecture of OEIS A091713 and the modulo 4 conjecture of OEIS A141117.
Analyzed functional equations defined by iterated compositions of generating functions.
Evaluated coefficient relations entirely within the ring of formal power series over integers.
Proved that every coefficient of the ordinary generating function F(x) for OEIS A091713 is odd.
Demonstrated that for n > 1, the coefficient a(n) of OEIS A141117 satisfies a(n) ≡ 0 (mod 4) if 3 divides n, and a(n) ≡ 2 (mod 4) otherwise.

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Implication

Mathematical analysis demonstrates modular congruences for sequence coefficients in OEIS A141117 and A091713, resolving two algebraic conjectures using formal power series.

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Yuan Chi (2026) studied this question.

synapsesocial.com/papers/6a8aae507677a341144474cf https://doi.org/10.5281/zenodo.22026845

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Proof of the Modulo 4 Conjecture for OEIS A141117 and of the Parity Conjecture for OEIS A091713

Key Points

No abstract yet

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Implication

Discussion

Cite This Study

Proof of the Modulo 4 Conjecture for OEIS A141117 and of the Parity Conjecture for OEIS A091713

Key Points

No abstract yet

Ask about this paper

Implication

Discussion

Cite This Study

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