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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. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..35.

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: A276023 A268822 A201926 * A050676 A010372 A199455

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

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Last modified March 29 14:58 EDT 2017. Contains 284270 sequences.