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%I #12 Oct 21 2015 05:58:05
%S 2,8,3,10,4,170,24,5,26,1520,17,6,19,3482,48,7,50,530,8,48842,3480,26,
%T 80,9,82,28,197,1574,49,10,227528,51,962,1126,120,11,122,4730624,577,
%U 10610,244,35,77563250,12,1728148040,37,1324,721,64080026,168,13,170,2024,199,4190210
%N The positive fundamental solutions x = x0(n) for the Pell equation x^2 - d*y^2 = +1 with odd y = y0(n). Then d coincides with d(n) = A007970(n).
%C The corresponding values y = y0(n) are given by A262026(n).
%C This is a proper subset of A033313 corresponding to D values from d(n) = A007970(n).
%C For the proof that d(n) = A007970(n), the products of Conway's 2-happy couples, see the W. Lang link under A007970.
%C If d(n) = A007970(n) is odd (necessarily congruent to 3 modulus 4) then x0(n) is even, and if d(n) is even (necessarily congruent to 0 modulus 8) then x0 is odd.
%F a(n)^2 - d(n)*y0(n)^2 = +1 with y0(n) = A262026(n) and d(n) = A007970(n). (x0(n) = a(n), y0(n)) are the positive fundamental solutions of this Pell equation x^2 - d*y^2 = +1 with odd y = y0.
%e For the first [d(n), x0(n), y0(n)] see A262026.
%Y Cf. A007970, A033313, A262026.
%K nonn
%O 1,1
%A _Wolfdieter Lang_, Oct 04 2015
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