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A033316 Value of D for incrementally largest values of minimal x satisfying Pell equation x^2-Dy^2=1. 18

%I

%S 1,2,5,10,13,29,46,53,61,109,181,277,397,409,421,541,661,1021,1069,

%T 1381,1549,1621,2389,3061,3469,4621,4789,4909,5581,6301,6829,8269,

%U 8941,9949,12541,13381,16069,17341,24049,24229,25309,29269,30781,32341,36061

%N Value of D for incrementally largest values of minimal x satisfying Pell equation x^2-Dy^2=1.

%C Equally, value of D for incrementally largest values of minimal y satisfying Pell equation x^2-Dy^2=1.

%C Values of n where A002349 (or A002350) sets a new record.

%H Ray Chandler, <a href="/A033316/b033316.txt">Table of n, a(n) for n = 1..93</a>

%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[ OddQ[n], n = 2*n]; s = FromContinuedFraction[ ContinuedFraction[ Sqrt[m], n]]; {Numerator[s], Denominator[s]}]; f[n_] := If[ !IntegerQ[ Sqrt[n]], PellSolve[n][[1]], 1]; a = b = -1; t = {}; Do[b = f[n]; If[b > a, t = Append[t, n]; a = b], {n, 1, 40500}]; t

%Y Cf. A000037, A033313, A033314, A033315, A002349, A002350.

%K nonn

%O 1,2

%A _Eric W. Weisstein_

%E More terms from _Robert G. Wilson v_, Apr 15 2003

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Last modified August 10 06:08 EDT 2022. Contains 356029 sequences. (Running on oeis4.)