Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Nov 22 2015 15:27:34
%S 1,17,1,49,21287,1,23,97,1,48727,161,151,1,21387679,241,1826021057,1,
%T 11692649642023,7,337,3903396217,1,294125365483681,17,449,7,
%U 1994828801,1,6399911,4798348971487087,577,119,7867888313,1,437071,161131189369,721,273849896195263,20783,262759
%N The y member of the positive proper fundamental solution (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - D(n)*y^2 = +8 for even D(n) = A264354(n).
%C The corresponding x2(n) value is given by A264438(n). The positive fundamental solution (x1(n), y1(n)) of the first class is given by (2*A261247(n), A261248(n)).
%C There is only one class of proper solutions for those D = D(n) = A264354(n) values leading to (x1(n), y1(n)) = (x2(n), y2(n)).
%e n=1: D(1) = 8, (2*2)^2 - 8*1^2 = +8. The first class positive fundamental solution was identical, thus there is only one class of proper solutions for D = 8.
%e n=5: D(5) = 124, (2*118521)^2 - 124*21287^2 = +8. The first class solution was (2*39)^2 - 124*7^2 = +8. Thus there are two classes, conjugated to each other for this D value.
%Y Cf. A264354, A261247 (x1/2), A261248 (y1), A264438 (x2/2), A263012 (odd D), A264349, A264350, A264351, A264353.
%K nonn
%O 1,2
%A _Wolfdieter Lang_, Nov 19 2015