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Search: id:A081232
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| A081232 |
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Let p = n-th prime of the form 4k+1, take smallest solution (x,y) to the Pellian equation x^2 - p*y^2 = 1 with x and y >= 1; sequence gives value of x. |
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+0
3
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| 9, 649, 33, 9801, 73, 2049, 66249, 1766319049, 2281249, 500001, 62809633, 201, 158070671986249, 1204353, 6083073, 25801741449, 46698728731849, 2499849, 2469645423824185801, 6224323426849, 393, 5848201, 1072400673
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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For n = 1, p = 5, x=9, y=4 since 9^2 = 5*4^2 + 1, so a(1) = 9.
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MATHEMATICA
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PellSolve[(m_Integer)?Positive] := Module[{cof, n, s}, cof = ContinuedFraction[Sqrt[m]]; n = Length[Last[cof]]; If[ OddQ[n], n = 2*n]; s = FromContinuedFraction[ContinuedFraction[Sqrt[m], n]]; {Numerator[s], Denominator[s]}]; First /@ PellSolve /@ Select[Prime@Range@54, Mod[ #, 4] == 1 &] (* Robert G. Wilson v *)
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CROSSREFS
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Values of y are in A082393. Cf. A082394. Equals A002350(p).
Values of y are in A082393. Cf. A082394, A081233. Equals A002350(p).
Sequence in context: A158881 A157597 A128795 this_sequence A020548 A091062 A015007
Adjacent sequences: A081229 A081230 A081231 this_sequence A081233 A081234 A081235
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Apr 18, 2003
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Feb 28 2006
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