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%I #11 Aug 11 2022 14:49:21
%S 2,53,314,1042,1685,1825,3281,4586,5521,6770,8597,9050,11509,13858,
%T 17498,20369,24737,28085,28130,29041,31226,33226,37141,37585,42965,
%U 47402,49205,53954,57125,58913,66193,71674,79682,85685,94421,100946,110410,113290,115202
%N Numbers k such that the equation x^2 - k*y^4 = -1 has a solution for which |y| > 2.
%C For k > 2, the equation x^2 - k*y^4 = -1 has at most one positive integer solution. If this solution (x, y) exists, we have v = y^2, where v is the smallest integer satisfying the Pell equation u^2 - k*v^2 = -1 (A130227).
%H Chen Jian Hua and Paul Voutier, <a href="https://arxiv.org/abs/1401.5450">Complete solution of the diophantine equation X^2 + 1 = dY^4 and a related family of quartic Thue equations</a>, arXiv:1401.5450 [math.NT], 2014-2018.
%e The equation x^2 - 2*y^4 = -1 has only two positive solutions (1, 1) and (239, 13), so 2 is in the sequence.
%Y Cf. A031396, A130227, A182468.
%K nonn
%O 1,1
%A _Jinyuan Wang_, Aug 09 2022