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%I #16 Apr 10 2019 13:43:38
%S 3,2,9,8,10,649,33,170,24,9801,1520,73,2049,3482,48,66249,530,
%T 1766319049,48842,3480,2281249,80,82,500001,62809633,201,227528,962,
%U 158070671986249,1204353,4730624,10610,6083073,77563250,25801741449
%N Let p = n-th prime, 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 Robert G. Wilson v, <a href="/A081233/b081233.txt">Table of n, a(n) for n = 1..10000</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)
%t PellSolve[(m_Integer)?Positive] := Module[{cf, n, s}, cf = ContinuedFraction[ Sqrt[m]]; n = Length[Last[cf]]; If[OddQ[n], n = 2*n]; s = FromContinuedFraction[ ContinuedFraction[ Sqrt[m], n]]; {Numerator[s], Denominator[s]}]; Table[ PellSolve[ Prime[n]][[1]], {n, 35}] (* _Robert G. Wilson v_, Jul 22 2005 *)
%t f[n_] := Block[{p = Prime[n]}, FindInstance[x^2 == p*y^2 + 1 && x > 0 && y > 0, {x, y}, Integers][[1, 1, 2]]]; Array[f, 40] (* _Robert G. Wilson v_, Nov 16 2012 *)
%Y Values of y are in A081234. Equals A002350(p). Cf. A082393.
%K easy,nonn
%O 1,1
%A _N. J. A. Sloane_, Apr 18 2003
%E a(8) - a(35) from _Robert G. Wilson v_, Jul 22 2005
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