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A179175 a(n) = least positive k such that Mordell's equation y^2 = x^3 - k has exactly n integral solutions. 13
3, 1, 2, 1331, 4, 216, 28, 54872, 116, 343, 828, 250047, 496, 71991296, 207 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The status of further terms is:

  15 integral solution: unknown

  16 integral solution: 503

  17 integral solution: unknown

  18 integral solution: 431

  19 integral solution: unknown

  20 integral solution: 2351

  21 integral solution: unknown

  22 integral solution: 3807

For least positive k such that equation y^2 = x^3 + k has exactly n integral solutions, see A179162.

If n is odd, then a(n) is perfect cube. [Ray Chandler]

LINKS

Table of n, a(n) for n=0..14.

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]

CROSSREFS

Cf. A081120, A081121, A179163-A179175.

Sequence in context: A088363 A300839 A143783 * A274635 A146524 A179656

Adjacent sequences:  A179172 A179173 A179174 * A179176 A179177 A179178

KEYWORD

nonn

AUTHOR

Artur Jasinski, Jun 30 2010

EXTENSIONS

Edited and a(7), a(11), a(13) added by Ray Chandler, Jul 11 2010

STATUS

approved

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Last modified November 15 01:22 EST 2019. Contains 329142 sequences. (Running on oeis4.)