A201047 Coordinates x of Mordell elliptic curves x^3-y^2 for primary extremal points with quadratic extensions over rationals.

1942, 2878, 3862, 6100, 8380, 18694, 31228, 93844, 111382, 117118, 129910, 143950, 186145, 210025, 575800, 1193740, 1248412, 1326025, 1388545, 1501504, 1697908, 1813660, 1946737, 2069353, 2151262, 2305180, 3864190, 3897622, 54054144, 61974313, 63546025

Offset: 1

Author

Artur Jasinski, Nov 26 2011

Keywords

• nonn

Comments

For y coordinates see A201269.

For distances d between cubes and squares see A201268.

Primary points in A200656.

For definition primary points see A200656.

For secondary terms in A200656 see A201048.

For successive quadratic extensions see A201278.

Theorem (*Artur Jasinski*):

Every particular coordinate x contained only one extremal point.

Proof (*Artur Jasinski*): Coordinate y is computable from the formula y(x) = round(sqrt(x^3)) and distance d between cube of x and square of y is computable from the formula d(x) = x^3-(round(sqrt(x^3)))^2.

Crossrefs

Cf. A201268, A201269, A200656.

Formula

a(n) = (A201268(n)+(A201269(n))^2)^(1/3).