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This research aims to uncover the arithmetic framework of the signed square-block sequence OEIS A392243 and its relation to pronic structures and elliptic fibers.

August 7, 2026Open Access

From Residue Dynamics to Arithmetic Fibers: The Pronic Structure of A392243 and Its Elliptic Sister Fiber

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This research aims to uncover the arithmetic framework of the signed square-block sequence OEIS A392243 and its relation to pronic structures and elliptic fibers.
Developed a folded pronic-distance formula for square-shell and pronic-cell coordinates.
Utilized PARI/GP and Magma for computer-assisted proofs and archived elliptic-curve certificates.
Classified adjacent-equal-magnitude seams and established specific mathematical laws and families.
Proved the absolute value of the signed sum at the critical threshold.
Derived fixed-offset laws and two genus-one twists for the weight-two sister sum.
Recorded collision provenance through certificate-typed edges and established the uniqueness result for noncentral d=-18.

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Implication

Develops the arithmetic structure of A392243, exploring its pronic and elliptic properties, indicating new mathematical insights.

Cite This Study

Jake Foth (2026) studied this question.

synapsesocial.com/papers/6a758c0f847ab6d26c01fd48 https://doi.org/10.5281/zenodo.21808754

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From Residue Dynamics to Arithmetic Fibers: The Pronic Structure of A392243 and Its Elliptic Sister Fiber

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Discussion

Implication

Cite This Study

From Residue Dynamics to Arithmetic Fibers: The Pronic Structure of A392243 and Its Elliptic Sister Fiber

Key Points

Discussion

Implication

Cite This Study

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