A081233 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 x.

3, 2, 9, 8, 10, 649, 33, 170, 24, 9801, 1520, 73, 2049, 3482, 48, 66249, 530, 1766319049, 48842, 3480, 2281249, 80, 82, 500001, 62809633, 201, 227528, 962, 158070671986249, 1204353, 4730624, 10610, 6083073, 77563250, 25801741449

Offset

1,1

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

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

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]][[1]], {n, 35}] (* Robert G. Wilson v, Jul 22 2005 *)
f[n_] := Block[{p = Prime[n]}, FindInstance[x^2 == p*y^2 + 1 && x > 0 && y > 0, {x, y}, Integers][[1, 1, 2]]]; Array[f, 40] (* Robert G. Wilson v, Nov 16 2012 *)

Crossrefs

Values of y are in A081234. Equals A002350(p). Cf. A082393.

Sequence in context: A268822 A201926 A288055 * A050676 A356185 A010372

Adjacent sequences: A081230 A081231 A081232 * A081234 A081235 A081236

Keyword

easy,nonn

Author

N. J. A. Sloane, Apr 18 2003

Extensions

a(8) - a(35) from Robert G. Wilson v, Jul 22 2005

Status

approved