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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 the rationals.

%I A200656 #51 May 10 2025 09:02:26
%S A200656 1942,2878,3862,6100,8380,11512,15448,18694,31228,93844,111382,117118,
%T A200656 129910,143950,186145,210025,375376,445528,468472,575800,844596,
%U A200656 1002438,1054062,1193740,1248412,1326025,1388545,1501504,1697908,1782112,1813660,1873888,1946737
%N A200656 Successive values x such that the Mordell elliptic curve x^3 - y^2 = d has extremal points with quadratic extension over the rationals.
%C A200656 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.
%C A200656 For y values see A200657.
%C A200656 For d values see A200658.
%C A200656 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.
%C A200656 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.
%C A200656 For successive secondary terms, see A201048.
%C A200656 A200216 is a subsequence of this sequence.
%H A200656 Peter J. C. Moses and Artur Jasinski, <a href="/A200656/b200656.txt">Table of n, a(n) for n = 1..185</a> (all terms below 10^9)
%Y A200656 Cf. A200216, A201047, A201048.
%Y A200656 Cf. A077119, A200657, A200658.
%K A200656 nonn
%O A200656 1,1
%A A200656 _Artur Jasinski_, Nov 20 2011