A099194 Least solution to the Pellian equation x^2 - k*y^2 = 1 (A002349) such that 2^2^n < y <= 2^2^(n+1).

2, 5, 10, 13, 29, 61, 109, 397, 1021, 2389, 6829, 25309, 82021, 271021, 952429

Offset

-1,1

Links

Table of n, a(n) for n=-1..13.

Mathematica

$MaxExtraPrecision = 512; 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]}]; f[n_] := If[ ! IntegerQ[ Sqrt[ n]], PellSolve[n][[2]], 0]; t = Table[0, {20}]; Do[a = Floor[ Log[2, Log[2, f[n]]]]; If[a < 20 && t[[a - 1]] == 0, t[[a - 1]] = n; Print[{a, n}]], {n, 10^7}]

Crossrefs

Cf. A002349, A002350, A069039, A099193.

Sequence in context: A328700 A018296 A033316 * A140411 A053353 A099792

Adjacent sequences: A099191 A099192 A099193 * A099195 A099196 A099197

Keyword

hard,nonn

Author

Robert G. Wilson v, Oct 02 2004

Status

approved