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.

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A356704 a(n) is the least k such that Mordell's equation y^2 = x^3 + k^3 has exactly 2*n+1 integral solutions.

Original entry on oeis.org

3, 7, 1, 2, 8, 329, 217, 506, 65, 260, 585
Offset: 0

Views

Author

Jianing Song, Aug 23 2022

Keywords

Comments

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(n) is the smallest index of 2*n+1 in A356706, of n in A356707, and of n+1 in A356708.

Examples

			a(4) = 8 since y^2 = x^3 + 8^3 has exactly 9 solutions (-8,0), (-7,+-13), (4,+-24), (8,+-32), and (184,+-2496), and the number of solutions to y^2 = x^3 + k^3 is not 9 for 0 < k < 8.

Crossrefs

Cf. A081119, A081120, A179162, A179175, A356705, A356706, A356707, A356708.

Formula

a(n) = A179162(2*n+1)^(1/3).

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.

Original entry on oeis.org

1, 11, 6, 38, 7, 63, 416, 2600, 10400, 93600
Offset: 0

Views

Author

Jianing Song, Aug 23 2022

Keywords

Comments

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.

Examples

			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.

Crossrefs

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

Formula

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

Extensions

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

A179165 Numbers n such that Mordell's equation y^2 = x^3 - n has exactly 4 integral solutions.

Original entry on oeis.org

4, 7, 11, 26, 48, 53, 55, 60, 63, 76, 109, 147, 180, 212, 215, 242, 256, 277, 362, 364, 375, 391, 405, 433, 448, 471, 476, 511, 535, 593, 615, 674, 680, 704, 728, 767, 782, 802, 831, 856, 875, 895, 900, 914, 931, 975, 991, 996, 1055, 1096, 1108, 1144, 1152
Offset: 1

Views

Author

Artur Jasinski, Jun 30 2010

Keywords

Links

Crossrefs

Cf. A081120, A081121, A179163-A179175.

Extensions

Edited by Ray Chandler, Jul 11 2010

A179166 Numbers n such that Mordell's equation y^2 = x^3 - n has exactly 6 integral solutions.

Original entry on oeis.org

28, 39, 47, 100, 104, 135, 152, 174, 191, 200, 244, 424, 440, 459, 732, 755, 804, 888, 984, 1048, 1075, 1084, 1236, 1259, 1287, 1322, 1432, 1503, 1668, 1763, 1792, 1812, 1951, 2160, 2224, 2344, 2367, 2440, 2468, 2496, 2556, 2692, 2695, 2699, 2727, 2799
Offset: 1

Views

Author

Artur Jasinski, Jun 30 2010

Keywords

Links

Crossrefs

Cf. A081120, A081121, A179163-A179175.

Extensions

Edited by Ray Chandler, Jul 11 2010

A179168 Numbers n such that Mordell's equation y^2 = x^3 - n has exactly 8 integral solutions.

Original entry on oeis.org

116, 307, 508, 516, 639, 964, 1192, 1208, 1588, 1607, 1692, 1719, 2036, 2548, 2575, 2708, 2888, 3231, 3376, 3623, 4598, 4743, 5319, 5508, 5823, 5872, 5887, 6012, 6400, 6551, 6691, 6823, 6911, 7375, 7600, 7740, 7900, 7975, 9127, 9408, 9455
Offset: 1

Views

Author

Artur Jasinski, Jun 30 2010

Keywords

Links

Crossrefs

Cf. A081120, A081121, A179163-A179175.

Extensions

Edited by Ray Chandler, Jul 11 2010

A179169 Numbers n such that Mordell's equation y^2 = x^3 - n has exactly 10 integral solutions.

Original entry on oeis.org

828, 944, 980, 1724, 2188, 3051, 3471, 3952, 3967, 4031, 4080, 5095, 5296, 5975, 6908, 7100, 7424, 7516, 7775, 8623
Offset: 1

Views

Author

Artur Jasinski, Jun 30 2010

Keywords

Links

Crossrefs

Cf. A081120, A081121, A179163-A179175.

Extensions

Edited by Ray Chandler, Jul 11 2010

A179170 Numbers n such that Mordell's equation y^2 = x^3 - n has exactly 12 integral solutions.

Original entry on oeis.org

496, 648, 676, 999, 1071, 1712, 1999, 2071, 3332, 4087, 4220, 5543, 6236, 6479, 8712, 9967
Offset: 1

Views

Author

Artur Jasinski, Jun 30 2010

Keywords

Links

Crossrefs

Cf. A081120, A081121, A179163-A179175.

Extensions

Edited by Ray Chandler, Jul 11 2010

A179171 Numbers n such that Mordell's equation y^2 = x^3 - n has exactly 14 integral solutions.

Original entry on oeis.org

207, 368, 775, 847, 1727, 4799, 7804, 8532, 9559
Offset: 1

Views

Author

Artur Jasinski, Jun 30 2010

Keywords

Links

Crossrefs

Cf. A081120, A081121, A179163-A179175.

Extensions

Edited by Ray Chandler, Jul 11 2010

A179172 Numbers n such that Mordell's equation y^2 = x^3 - n has exactly 16 integral solutions.

Original entry on oeis.org

503, 1439
Offset: 1

Views

Author

Artur Jasinski, Jun 30 2010

Keywords

Links

Crossrefs

Cf. A081120, A081121, A179163-A179175.

Extensions

Edited by Ray Chandler, Jul 11 2010

A179173 Numbers n such that Mordell's equation y^2 = x^3 - n has exactly 18 integral solutions.

Original entry on oeis.org

431, 9748
Offset: 1

Views

Author

Artur Jasinski, Jun 30 2010

Keywords

Links

Crossrefs

Cf. A081120, A081121, A179163-A179175.

Extensions

Edited by Ray Chandler, Jul 11 2010
Previous Showing 21-30 of 30 results.

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