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A081231
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Let p = n-th prime of the form 4k+3, 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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4
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2, 8, 10, 170, 24, 1520, 3482, 48, 530, 48842, 3480, 80, 82, 227528, 962, 4730624, 10610, 77563250, 1728148040, 64080026, 168, 4190210, 8994000, 16266196520, 278354373650, 224, 226, 6195120, 3674890, 139128, 115974983600, 138274082
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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EXAMPLE
| For n=3, p = 11, x=10, y=3 since we have 10^2 = 11*3^2 + 1, so a(3) = 10.
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MATHEMATICA
| 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]}]; Transpose[ PellSolve /@ Select[ Prime[ Range[72]], Mod[ #, 4] == 3 &]][[1]] (from Robert G. Wilson v Sep 02 2004)
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CROSSREFS
| Values of y are in A081231. Equals A002350(p). Cf. A082393.
Sequence in context: A071184 A174153 A171976 * A121715 A121714 A064611
Adjacent sequences: A081228 A081229 A081230 * A081232 A081233 A081234
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KEYWORD
| easy,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 18, 2003
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 02 2004
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