A200656 Successive values x such that the Mordell elliptic curve x^3 - y^2 = d has extremal points with quadratic extension over the rationals.

1942, 2878, 3862, 6100, 8380, 11512, 15448, 18694, 31228, 93844, 111382, 117118, 129910, 143950, 186145, 210025, 375376, 445528, 468472, 575800, 844596, 1002438, 1054062, 1193740, 1248412, 1326025, 1388545

Offset

1,1

Comments

Definition: Extremal points on the Mordell elliptic curve x^3 - y^2 = d are points (x,y) such that x^3 - round(sqrt(x^3))^2 = d. For values d for successive x independent of the extensions see A077119.

For y values see A200657.

For d values see A200658.

Definition: Secondary terms occur when there exist integers k such that A200656 is divisible by k^2, A200657 is divisible by k^3 and A200658 is divisible by k^6.

Terms free of such k are primary terms; see A201047. Secondary terms are, e.g., a(6)=a(2)*2^2, a(7)=a(3)*2^2, a(17)=a(10)*2^2, a(18)=a(11)*2^2, a(19)=a(12)*2^2, a(21)=a(10)*3^2.

For successive secondary terms, see A201048.

A200216 is a subsequence of this sequence.

Links

Peter J. C. Moses and Artur Jasinski, Complete list of extremal points on Mordell curves x^3 - y^2 = d with quadratic extensions in range x from 1 to 10^9

Crossrefs

Cf. A200216, A201047.

Cf. A077119, A200657, A200658.

Sequence in context: A202529 A236714 A203890 * A201047 A269039 A300199

Adjacent sequences: A200653 A200654 A200655 * A200657 A200658 A200659

Keyword

nonn

Author

Artur Jasinski, Nov 20 2011

Status

approved