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.

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

Offset: 0

Author

Jianing Song, Aug 23 2022

Keywords

• nonn
• hard
• more

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).