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, 1501504, 1697908, 1782112, 1813660, 1873888, 1946737

Offset: 1

Author

Artur Jasinski, Nov 20 2011

Keywords

• nonn

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, Table of n, a(n) for n = 1..185 (all terms below 10^9)

Crossrefs

Cf. A200216, A201047, A201048.

Cf. A077119, A200657, A200658.