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%I #13 Jun 10 2014 14:23:59
%S 9,649,33,9801,73,2049,66249,1766319049,2281249,500001,62809633,201,
%T 158070671986249,1204353,6083073,25801741449,46698728731849,2499849,
%U 2469645423824185801,6224323426849,393,5848201,1072400673
%N Let p = n-th prime of the form 4k+1, take smallest solution (x,y) to the Pellian equation x^2 - p*y^2 = 1 with x and y >= 1; sequence gives value of x.
%H Vincenzo Librandi, <a href="/A081232/b081232.txt">Table of n, a(n) for n = 1..2000</a>
%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%e For n = 1, p = 5, x=9, y=4 since 9^2 = 5*4^2 + 1, so a(1) = 9.
%t PellSolve[(m_Integer)?Positive] := Module[{cof, n, s}, cof = ContinuedFraction[Sqrt[m]]; n = Length[Last[cof]]; If[ OddQ[n], n = 2*n]; s = FromContinuedFraction[ContinuedFraction[Sqrt[m], n]]; {Numerator[s], Denominator[s]}]; First /@ PellSolve /@ Select[Prime@Range@54, Mod[ #, 4] == 1 &] (* _Robert G. Wilson v_ *)
%Y Values of y are in A082393. Cf. A082394, A081233. Equals A002350(p).
%K easy,nonn
%O 1,1
%A _N. J. A. Sloane_, Apr 18, 2003
%E More terms from _Robert G. Wilson v_, Feb 28 2006
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