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A033315 Incrementally largest values of minimal x satisfying Pell equation x^2-Dy^2=1. 17
1, 3, 9, 19, 649, 9801, 24335, 66249, 1766319049, 158070671986249, 2469645423824185801, 159150073798980475849, 838721786045180184649, 25052977273092427986049, 3879474045914926879468217167061449 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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.

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 = 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-Fran├žois Alcover, Nov 21 2020, after N. J. A. Sloane in A002349 *)

CROSSREFS

Records in A033313 (or A002350).

Cf. A033313, A033314, A002349, A002350.

Cf. A033316 (corresponding values of D)

Sequence in context: A146066 A164283 A178963 * A200612 A073716 A174866

Adjacent sequences:  A033312 A033313 A033314 * A033316 A033317 A033318

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified June 16 12:29 EDT 2021. Contains 345057 sequences. (Running on oeis4.)