A033316 Value of D for incrementally largest values of minimal x satisfying Pell equation x^2-Dy^2=1.

1, 2, 5, 10, 13, 29, 46, 53, 61, 109, 181, 277, 397, 409, 421, 541, 661, 1021, 1069, 1381, 1549, 1621, 2389, 3061, 3469, 4621, 4789, 4909, 5581, 6301, 6829, 8269, 8941, 9949, 12541, 13381, 16069, 17341, 24049, 24229, 25309, 29269, 30781, 32341, 36061

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Equally, value of D for incrementally largest values of minimal y satisfying Pell equation x^2-Dy^2=1.

Values of n where A002349 (or A002350) sets a new record.

Links

• Peter J. Taylor, Table of n, a(n) for n = 1..334 (terms 1..93 from Ray Chandler).
• Eric Weisstein's World of Mathematics, Pell Equation.

Crossrefs

Cf. A000037, A033313, A033314, A033315, A002349, A002350.

Programs

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]}]; f[n_] := If[ !IntegerQ[ Sqrt[n]], PellSolve[n][[1]], 1]; a = b = -1; t = {}; Do[b = f[n]; If[b > a, t = Append[t, n]; a = b], {n, 1, 40500}]; t

Extensions

More terms from Robert G. Wilson v, Apr 15 2003