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

1,1

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.

Links

Table of n, a(n) for n=1..31.

Formula

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

Crossrefs

Cf. A201268, A201269, A200656.

Sequence in context: A236714 A203890 A200656 * A269039 A300199 A252151

Adjacent sequences: A201044 A201045 A201046 * A201048 A201049 A201050

Keyword

nonn

Author

Artur Jasinski, Nov 26 2011

Status

approved