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A200656 Successive values x such that the Mordell elliptic curve x^3 - y^2 = d has extremal points with quadratic extension over rationals. 9
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 (list; graph; refs; listen; history; text; internal format)
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 subset 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.

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

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Last modified April 3 23:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)