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A033315
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Incrementally largest values of minimal x satisfying Pell equation x^2-Dy^2=1.
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17
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1, 3, 9, 19, 649, 9801, 24335, 66249, 1766319049, 158070671986249, 2469645423824185801, 159150073798980475849, 838721786045180184649, 25052977273092427986049, 3879474045914926879468217167061449
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OFFSET
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1,2
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LINKS
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T. D. Noe and Ray Chandler, Table of n, a(n) for n = 1..62 (first 50 terms from T. D. Noe)
Eric Weisstein's World of Mathematics, Pell Equation.
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MATHEMATICA
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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]}];
xx = DeleteCases[PellSolve /@ Range[10^5], {}][[All, 1]];
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 *)
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CROSSREFS
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Records in A033313 (or A002350).
Cf. A033313, A033314, A002349, A002350.
Cf. A033316 (corresponding values of D)
Sequence in context: A146066 A164283 A178963 * A200612 A355136 A073716
Adjacent sequences: A033312 A033313 A033314 * A033316 A033317 A033318
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein
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STATUS
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approved
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