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%I #12 Feb 25 2015 11:32:58
%S 5,7,13,9,21,11,17,29,19,15,31,37,17,27,33,23,29,21,41,47,37,23,43,33,
%T 49,55,51,31,41,69,53,29,43,59,35,31,45,61,41,67,85,57,47,63,43,53,35,
%U 75,93,37,71,61,83,47,89,39,73,53,63,79,49,85,69,97,103,109,55
%N Fundamental positive solution x = x2(n) of the second class of the Pell equation x^2 - 2*y^2 = -A007522(n), n >= 1 (primes congruent to 7 mod 8).
%C The corresponding term y = y2(n) of this fundamental solution of the second class of the (generalized) Pell equation x^2 - 2*y^2 = -A007522(n) = -(1 + A139487(n)*8) is given in 2*A255234(n).
%C For comments and the Nagell reference see A254938.
%F a(n)^2 - 2*(2*A255234(n))^2 = -A007522(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.
%F a(n) = -(3*A254938(n) - 4*2*A255232(n)), n >= 1.
%e The first pairs [x2(n), y2(n)] of the fundamental positive solutions of this second class are (the prime A007522(n) appears as first entry):
%e [7, [5, 4]], [23, [7, 6]], [31, [13, 10]],
%e [47, [9, 8]], [71, [21, 16]], [79, [11, 10]], [103, [17, 14]], [127, [29, 22]],
%e [151, [19, 16]], [167, [15, 14]],
%e [191, [31, 24]], [199, [37, 28]],
%e [223, [17, 16]], [239, [27, 22]],
%e [263, [33, 26]], [271, [23, 20]],
%e [311, [29, 24]], [359, [21, 20]],
%e [367, [41, 32]], [383, [47, 36]],
%e [431, [37, 30]], [439, [23, 22]],
%e [463, [43, 34]], [479, [33, 28]], ...
%e n= 4: 9^2 - 2*(2*4)^2 = -47 = -A007522(4).
%e a(4) = -(3*5 - 4*(2*3)) = 24 - 15 = 9.
%Y Cf. A007522, A139487, 2*A255234, A254938, 2*A255232, A255247, A254936.
%K nonn,look,easy
%O 1,1
%A _Wolfdieter Lang_, Feb 18 2015
%E More terms from _Colin Barker_, Feb 23 2015
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