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%I A033315 #26 Nov 03 2023 11:17:24
%S A033315 1,3,9,19,649,9801,24335,66249,1766319049,158070671986249,
%T A033315 2469645423824185801,159150073798980475849,838721786045180184649,
%U A033315 25052977273092427986049,3879474045914926879468217167061449
%N A033315 Incrementally largest values of minimal x satisfying Pell equation x^2 - D*y^2 = 1.
%H A033315 Ray Chandler, <a href="/A033315/b033315.txt">Table of n, a(n) for n = 1..62</a> (first 50 terms from T. D. Noe)
%H A033315 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PellEquation.html">Pell Equation</a>.
%t A033315 PellSolve[(m_Integer)?Positive] := Module[{cf, n, s}, cf = ContinuedFraction[Sqrt[m]]; n = Length[Last[cf]]; If[n == 0, Return[{}]]; If[OddQ[n], n = 2 n]; s = FromContinuedFraction[ ContinuedFraction[ Sqrt[m], n]]; {Numerator[s], Denominator[s]}];
%t A033315 xx = DeleteCases[PellSolve /@ Range[10^5], {}][[All, 1]];
%t A033315 Reap[Module[{x, record = 0}, Sow[1]; For[i = 1, i <= Length@xx, i++, x = xx[[i]]; If[x > record, record = x; Sow[x]]]]][[2, 1]] (* _Jean-François Alcover_, Nov 21 2020, after _N. J. A. Sloane_ in A002349 *)
%Y A033315 Records in A033313 (or A002350).
%Y A033315 Cf. A033313, A033314, A002349, A002350.
%Y A033315 Cf. A033316 (corresponding values of D).
%K A033315 nonn,easy
%O A033315 1,2
%A A033315 _Eric W. Weisstein_

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