%I #11 Feb 15 2015 13:52:14
%S 7,13,19,17,15,25,23,29,25,23,35,43,31,27,49,37,47,55,31,45,61,37,35,
%T 59,49,67,47,45,53,63,71,47,43,77,57,85,55,53,51,49,73,61,81,89,57,97,
%U 51,67,87
%N Fundamental positive solution x = x2(n) of the second class of the Pell equation x^2 - 2*y^2 = A007519(n), n >= 1 (primes congruent to 1 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 = A007519(n) = 1 + 8*A005123(n) is given in 2*A254763(n).
%C For comments and the Nagell reference see A254760.
%F a(n)^2 - 2*(2*A254763(n))^2 = A007519(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.
%F a(n) = 3*A254760(n) - 8*A254761(n), n >= 1.
%e The first pairs [x2(n), y2(n)] of the fundamental positive solutions of the second class are (we list the prime A007519(n) as first entry):
%e [17, [7, 4]], [41, [13, 8]], [73, [19, 12]], [89, [17, 10]], [97, [15, 8]], [113, [25, 16]], [137, [23, 14]], [193, [29, 18]], [233, [25, 14]], [241, [23, 12]], [257, [35, 22]], [281, [43, 28]], [313, [31, 18]], [337, [27, 14]], [353, [49, 32]], [401, [37, 22]], [409, [47, 30]], ...
%e a(4) = 3*11 - 8*2 = 17.
%Y Cf. A007519, A005123, 2*A254763, A254760, 2*A254761.
%K nonn,easy
%O 1,1
%A _Wolfdieter Lang_, Feb 10 2015