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A033315 Incrementally largest values of minimal x satisfying Pell equation x^2-Dy^2=1. 17

%I

%S 1,3,9,19,649,9801,24335,66249,1766319049,158070671986249,

%T 2469645423824185801,159150073798980475849,838721786045180184649,

%U 25052977273092427986049,3879474045914926879468217167061449

%N Incrementally largest values of minimal x satisfying Pell equation x^2-Dy^2=1.

%H T. D. Noe and 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PellEquation.html">Pell Equation</a>.

%t 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 xx = DeleteCases[PellSolve /@ Range[10^5], {}][[All, 1]];

%t 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 Records in A033313 (or A002350).

%Y Cf. A033313, A033314, A002349, A002350.

%Y Cf. A033316 (corresponding values of D)

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_

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Last modified July 26 13:40 EDT 2021. Contains 346294 sequences. (Running on oeis4.)