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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.
1
3, 7, 1, 2, 8, 329, 217, 506, 65, 260, 585
OFFSET
0,1
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.
FORMULA
a(n) = A179162(2*n+1)^(1/3).
EXAMPLE
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.
KEYWORD
nonn,hard,more
AUTHOR
Jianing Song, Aug 23 2022
STATUS
approved