A081234 Let p = n-th prime, take smallest solution (x,y) to the Pellian equation x^2 - p*y^2 = 1 with x and y >= 1; sequence gives value of y.

2, 1, 4, 3, 3, 180, 8, 39, 5, 1820, 273, 12, 320, 531, 7, 9100, 69, 226153980, 5967, 413, 267000, 9, 9, 53000, 6377352, 20, 22419, 93, 15140424455100, 113296, 419775, 927, 519712, 6578829, 2113761020, 140634693, 3726964292220, 5019135, 13, 190060

Offset: 1

Author

N. J. A. Sloane, Apr 18 2003

Keywords

• easy
• nonn

Links

• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Values of x are in A081233. Equals A002349(p). Cf. A082393.

Programs

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]}]; Table[ PellSolve[ Prime[n]][[2]], {n, 40}] (* Robert G. Wilson v, Jul 22 2005 *)

Extensions

More terms (a(8) - a(40)) from Robert G. Wilson v, Jul 22 2005