A081231 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.

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

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

For n=3, p = 11, x=10, y=3 since we have 10^2 = 11*3^2 + 1, so a(3) = 10.

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]] (* Robert G. Wilson v, Sep 02 2004 *)

Crossrefs

Values of y are in A082394. Equals A002350(p). Cf. A082393.

Sequence in context: A174153 A171976 A362278 * A229128 A121715 A121714

Adjacent sequences: A081228 A081229 A081230 * A081232 A081233 A081234

Keyword

easy,nonn

Author

N. J. A. Sloane, Apr 18 2003

Extensions

More terms from Robert G. Wilson v, Sep 02 2004

Status

approved