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%I #7 Feb 24 2015 05:34:52
%S 9,11,13,19,25,15,21,23,35,41,25,21,37,49,23,39,29,25,57,35,27,59,65,
%T 33,43,29,49,55,51,41,37,69,81,39,59,35,65,71,77,83,51,67,47,43,79,39,
%U 97,69,49,59
%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 A254937(n).
%C For comments and the Nagell reference see A254934.
%F a(n)^2 - 2*A254937(n)^2 = -A007519(n) gives the second smallest positive (proper) solution of this (generalized) Pell equation.
%F a(n) = -(3*A254934(n) - 4*A254935(n)), n >= 1.
%e The first pairs [x2(n), y2(n)] of the fundamental positive solutions of this second class are (the prime A007519(n) appears as first entry):
%e [17, [9, 7]], [41, [11, 9]], [73, [13, 11]],
%e [89, [19, 15]], [97, [25, 19]], [113, [15, 13]],
%e [137, [21, 17]], [193, [23, 19]], [233, [35, 27]],
%e [241, [41, 31]], [257, [25, 21]], [281, [21, 19]],
%e [313, [37, 29]], [337, [49, 37]], [353, [23, 21]],
%e [401, [39, 31]], [409, [29, 25]], [433, [25, 23]],
%e [449, [57, 43]], [457, [35, 29]], [521, [27, 25]],
%e [569, [59, 45]], [577, [65, 49]], [593, [33, 29]],
%e [601, [43, 35]], [617, [29, 27]], [641, [49, 39]], ...
%e a(4) = -(3*3 - 4*7) = 28 - 9 = 19.
%Y Cf. A007519, A005123, A254937, A254934, A254935, A255233, A255247.
%K nonn,look,easy
%O 1,1
%A _Wolfdieter Lang_, Feb 18 2015
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