OFFSET
0,2
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.
FORMULA
a(n) = A179175(2*n+1)^(1/3).
EXAMPLE
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
KEYWORD
nonn,hard,more
AUTHOR
Jianing Song, Aug 23 2022
EXTENSIONS
a(7)-a(9) from Jose Aranda, Aug 05 2024
STATUS
approved