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 A033313 Smallest positive integer x satisfying the Pell equation x^2 - D*y^2 = 1 for nonsquare D and positive y. 24
 3, 2, 9, 5, 8, 3, 19, 10, 7, 649, 15, 4, 33, 17, 170, 9, 55, 197, 24, 5, 51, 26, 127, 9801, 11, 1520, 17, 23, 35, 6, 73, 37, 25, 19, 2049, 13, 3482, 199, 161, 24335, 48, 7, 99, 50, 649, 66249, 485, 89, 15, 151, 19603, 530, 31, 1766319049, 63, 8, 129, 65, 48842, 33 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 S. R. Finch, Class number theory [Cached copy, with permission of the author] H. W. Lenstra, jr., Solving the Pell Equation F. Richman & R. Mines, Pell's equation Derek Smith, Historical Overview of Pell Equations Eric Weisstein's World of Mathematics, Pell Equation FORMULA a(n) = sqrt(1 + A000037(n)*A033317(n)^2), or a(n) = sqrt(1 + (n + floor(1/2 + sqrt(n)))*A033317(n)^2). - Zak Seidov, Oct 24 2013 MAPLE F:= proc(d) local r, Q; uses numtheory;   Q:= cfrac(sqrt(d), 'periodic', 'quotients'):   r:= nops(Q);   if r::odd then     numer(cfrac([op(Q), op(Q), op(Q[1..-2])]))   else     numer(cfrac([op(Q), op(Q[1..-2])]));   fi end proc: map(F, remove(issqr, [\$1..100])); # Robert Israel, May 17 2015 MATHEMATICA PellSolve[(m_Integer)?Positive] := Module[{cf, n, s}, cf = ContinuedFraction[Sqrt[m]]; n = Length[Last[cf]]; If[n == 0, Return[{}]]; If[OddQ[n], n = 2n]; s = FromContinuedFraction[ContinuedFraction[Sqrt[m], n]]; {Numerator[s], Denominator[s]}]; A033313 = DeleteCases[PellSolve /@ Range, {}][[All, 1]] (* Jean-François Alcover, Nov 21 2020, after N. J. A. Sloane in A002350 *) CROSSREFS See A033317 (for y's). Cf. A000037, A002350, A077232, A077233. Sequence in context: A064614 A234747 A016650 * A231442 A319107 A228323 Adjacent sequences:  A033310 A033311 A033312 * A033314 A033315 A033316 KEYWORD nonn AUTHOR EXTENSIONS Offset switched to 1 by R. J. Mathar, Sep 21 2009 Name corrected by Wolfdieter Lang, Sep 03 2015 STATUS approved

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Last modified January 27 08:35 EST 2021. Contains 340460 sequences. (Running on oeis4.)