cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A233379 List of x coordinates of infinite family of points on the Mordell curve x^3-y^2=d over quadratic field Sqrt[13].

Original entry on oeis.org

2860, 7105509268, 11974446516944860, 20174575425969672027268, 33990165031985542839913742860, 57266698026205846472927526499559668, 96483047367913681099665838319655915836860, 162554831171498439057365601894265975887204106468, 273872704667306430073374450872850543845308421200346860
Offset: 1

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Author

Artur Jasinski, Dec 08 2013

Keywords

Comments

a(1)=A202054(5).
For y values see A233392
For d values see A233391

Crossrefs

Cf. A233391, A233392, A202054.

Formula

a(n)=(13 (-1 + 4 t[n] + t[n]^2)) where t[n] satisfies the linear recurrence t[n]=1299 t[n-1]-1299 t[n-2] + t[n-2] with t[1]=13, t[2]=23377, t[3]=30349813.
(A233379(n))^3-(A233392(n))^2=A233391(n).

A202055 Smallest y such that Mordell's elliptic curve x^3-y^2=d (for positive d) has an integral point in the quadratic extension sqrt(A202057(n)).

Original entry on oeis.org

100, 476425, 800, 46823500, 152945, 1304261335, 128375, 17793340084
Offset: 1

Views

Author

Artur Jasinski, Dec 10 2011

Keywords

Comments

The existence of such y for each A202057(n) is conjectural following the conjecture in A201278.
For x values see A202054.
For d values see A202056.

Crossrefs

Cf. A201278, A202054, A202056, A202057.

A202056 Smallest d such that Mordell's elliptic curve x^3-y^2=d (for positive d) has an integral point in the quadratic extension sqrt(A202057(n)).

Original entry on oeis.org

648, 219375, 41472, 6021000, 1482975, 69641775, 3888000, 483568488
Offset: 1

Views

Author

Artur Jasinski, Dec 10 2011

Keywords

Comments

The existence of such d for each A202057(n) is conjectural following the conjecture in A201278.
For x values see A202054.
For y values see A202055.

Crossrefs

Cf. A201278, A202054, A202055, A202057.

Formula

a(n) = A202054(n)^3 - A202055(n)^2
Showing 1-3 of 3 results.

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