A081232 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.

9, 649, 33, 9801, 73, 2049, 66249, 1766319049, 2281249, 500001, 62809633, 201, 158070671986249, 1204353, 6083073, 25801741449, 46698728731849, 2499849, 2469645423824185801, 6224323426849, 393, 5848201, 1072400673

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

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

Example

For n = 1, p = 5, x=9, y=4 since 9^2 = 5*4^2 + 1, so a(1) = 9.

Mathematica

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 *)

Crossrefs

Values of y are in A082393. Cf. A082394, A081233. Equals A002350(p).

Sequence in context: A128795 A323425 A191510 * A020548 A091062 A221133

Adjacent sequences: A081229 A081230 A081231 * A081233 A081234 A081235

Keyword

easy,nonn

Author

N. J. A. Sloane, Apr 18, 2003

Extensions

More terms from Robert G. Wilson v, Feb 28 2006

Status

approved