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A365811 Numbers k >= 0 such that Mordell's equation y^2 = k^3 + x*(x + 1)/2 has an integral solution for a pair (x >= 0, y >= 0).

%I A365811 #31 Sep 25 2023 08:14:44
%S A365811 0,1,2,4,9,11,12,14,16,25,26,35,36,38,40,45,49,57,62,64,69,71,74,81,
%T A365811 84,85,88,95,96,97,100,107,109,117,120,121,122,134,136,144,145,146,
%U A365811 155,156,157,169,170,172,179,180,191,196,201,213,217,225,230,240,242,244
%N A365811 Numbers k >= 0 such that Mordell's equation y^2 = k^3 + x*(x + 1)/2 has an integral solution for a pair (x >= 0, y >= 0).
%C A365811 If there is a solution, then y >= k^(3/2). For k = r^2, the least solution is (x = 0, y = r^3).
%e A365811 k = 4 is a term: 8^2 = 4^3.
%e A365811 k = 11 is a term: 39^2 = 11^3 + 19*20/2.
%o A365811 (PARI) isOK(k) = { []<>bnfisintnorm(bnfinit(x^2-2),16*k^3-2)} \\ _Thomas Scheuerle_, Sep 19 2023
%Y A365811 Cf. A000217, A000290, A000578, A054504.
%K A365811 nonn
%O A365811 1,3
%A A365811 _Ctibor O. Zizka_, Sep 19 2023