A179162 -id:A179162 - cp's OEIS frontend

A356705 a(n) is the least k such that Mordell's equation y^2 = x^3 - k^3 has exactly 2*n+1 integral solutions.

1, 11, 6, 38, 7, 63, 416, 2600, 10400, 93600

Offset: 0

Jianing Song, Aug 23 2022

a(n) is the least k such that y^2 = x^3 - k^3 has exactly n solutions with y positive, or exactly n+1 solutions with y nonnegative.

			a(1) = 11 since y^2 = x^3 - 11^3 has exactly 3 solutions (11,0) and (443,+-9324), and the number of solutions to y^2 = x^3 - k^3 is not 3 for 0 < k < 11.
a(2) = 6 since y^2 = x^3 - 6^3 has exactly 5 solutions (6,0), (10,+-28), and (33,+-189), and the number of solutions to y^2 = x^3 - k^3 is not 5 for 0 < k < 6.
a(4) = 7 since y^2 = x^3 - 7^3 has exactly 9 solutions (7,0), (8,+-13), (14,+-49), (28,+-147), and (154,+-1911), and the number of solutions to y^2 = x^3 - k^3 is not 9 for 0 < k < 7.

Cf. A081119, A081120, A179162, A179175, A356704.

a(n) = A179175(2*n+1)^(1/3).

a(7)-a(9) from Jose Aranda, Aug 05 2024

A179153 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 10 integral solutions.

Original entry on oeis.org

9, 217, 252, 360, 548, 576, 836, 892, 1009, 1225, 1729, 1764, 1772, 2024, 2201, 2296, 2304, 2312, 2600, 3185, 3489, 3592, 4364, 4600, 4625, 4964, 5624, 5696, 5776, 5913, 6057, 6372, 6489, 6513, 6561, 6616, 6713, 6912, 7388, 8100, 8809, 9000, 9024, 9052

Offset: 1

Artur Jasinski, Jun 30 2010

nonn

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Cf. A054504, A081119, A179145-A179162.

Edited by Ray Chandler, Jul 11 2010

A179154 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 12 integral solutions.

Original entry on oeis.org

73, 100, 113, 388, 1304, 1809, 1900, 2052, 2241, 3356, 3753, 4672, 5328, 6625, 6856, 6921, 7948, 8433, 8673, 9936

Offset: 1

Artur Jasinski, Jun 30 2010

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Cf. A054504, A081119, A179145-A179162.

Edited by Ray Chandler, Jul 11 2010

A179155 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 14 integral solutions.

Original entry on oeis.org

316, 568, 1016, 1872, 4329, 4825, 6400, 7353, 8289

Offset: 1

Artur Jasinski, Jun 30 2010

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Cf. A054504, A081119, A179145-A179162.

Edited by Ray Chandler, Jul 11 2010

A179157 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 16 integral solutions.

Original entry on oeis.org

17, 1088, 3033, 3664, 3844, 4356, 4977, 5400, 7232, 7568, 7785, 9297

Offset: 1

Artur Jasinski, Jun 30 2010

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Cf. A054504, A081119, A179145-A179162.

Edited by Ray Chandler, Jul 11 2010

A179158 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 18 integral solutions.

Original entry on oeis.org

297, 873, 1305, 2628, 3969, 8281, 8676

Offset: 1

Artur Jasinski, Jun 30 2010

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Cf. A054504, A081119, A179145-A179162.

Edited by Ray Chandler, Jul 11 2010

A179159 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 20 integral solutions.

Original entry on oeis.org

2817, 4112, 4312, 5841

Offset: 1

Artur Jasinski, Jun 30 2010

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Cf. A054504, A081119, A179145-A179162.

Edited by Ray Chandler, Jul 11 2010

A179160 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 22 integral solutions.

Original entry on oeis.org

1737, 3025, 7057, 8225

Offset: 1

Artur Jasinski, Jun 30 2010

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Cf. A054504, A081119, A179145-A179162.

Edited by Ray Chandler, Jul 11 2010

A179161 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 24 integral solutions.

Original entry on oeis.org

4481, 8900

Offset: 1

Artur Jasinski, Jun 30 2010

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Cf. A054504, A081119, A179145-A179162.

Edited by Ray Chandler, Jul 11 2010

cp's OEIS Frontend

A356705 a(n) is the least k such that Mordell's equation y^2 = x^3 - k^3 has exactly 2*n+1 integral solutions.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

Extensions

A179153 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 10 integral solutions.

Views

Author

Keywords

Links

Crossrefs

Extensions

A179154 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 12 integral solutions.

Views

Author

Keywords

Links

Crossrefs

Extensions

A179155 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 14 integral solutions.

Views

Author

Keywords

Links

Crossrefs

Extensions

A179157 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 16 integral solutions.

Views

Author

Keywords

Links

Crossrefs

Extensions

A179158 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 18 integral solutions.

Views

Author

Keywords

Links

Crossrefs

Extensions

A179159 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 20 integral solutions.

Views

Author

Keywords

Links

Crossrefs

Extensions

A179160 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 22 integral solutions.

Views

Author

Keywords

Links

Crossrefs

Extensions

A179161 Numbers n such that Mordell's equation y^2 = x^3 + n has exactly 24 integral solutions.

Views

Author

Keywords

Links

Crossrefs

Extensions