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

Author

N. J. A. Sloane, Apr 18 2003

Keywords

• easy
• nonn

Examples

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

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)

Crossrefs

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

Programs

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 *)

Extensions

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