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A099194 Least solution to the Pellian equation x^2 - k*y^2 = 1 (A002349) such that 2^2^n < y <= 2^2^(n+1). 0

%I

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

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

%t $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}]

%Y Cf. A002349, A002350, A069039, A099193.

%K hard,nonn

%O -1,1

%A _Robert G. Wilson v_, Oct 02 2004

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Last modified September 28 04:28 EDT 2022. Contains 357063 sequences. (Running on oeis4.)