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Search: id:A033316
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| A033316 |
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Value of D for incrementally largest values of minimal x satisfying Pell equation x^2-Dy^2=1. |
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+0
5
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| 1, 2, 5, 10, 13, 29, 46, 53, 61, 109, 181, 277, 397, 409, 421, 541, 661, 1021, 1069, 1381, 1549, 1621, 2389, 3061, 3469, 4621, 4789, 4909, 5581, 6301, 6829, 8269, 8941, 9949, 12541, 13381, 16069, 17341, 24049, 24229, 25309, 29269, 30781, 32341, 36061
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Equally, value of D for incrementally largest values of minimal y satisfying Pell equation x^2-Dy^2=1.
Values of n where A002349 (or A002350) sets a new record.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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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[ 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
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CROSSREFS
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Cf. A033313, A033314, A033315, A002349, A002350.
Sequence in context: A103188 A064392 A018296 this_sequence A099194 A140411 A053353
Adjacent sequences: A033313 A033314 A033315 this_sequence A033317 A033318 A033319
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) Apr 15 2003
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