A033319 Incrementally largest values of minimal y satisfying Pell equation x^2-Dy^2=1.

0, 2, 4, 6, 180, 1820, 3588, 9100, 226153980, 15140424455100, 183567298683461940, 9562401173878027020, 42094239791738433660, 1238789998647218582160, 189073995951839020880499780706260

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Records in A033317 (or A002349).

Links

• Ray Chandler, Table of n, a(n) for n = 1..63
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
• Eric Weisstein's World of Mathematics, Pell Equation.

Crossrefs

Cf. A000037, A033317, A033318, A002349, A002350, A033316.

Programs

Mathematica

PellSolve[(m_Integer)?Positive] := Module[{cf, n, s}, cf = ContinuedFraction[Sqrt[m]]; n = Length[Last[cf]]; If[n == 0, Return[{}]]; If[OddQ[n], n = 2 n]; s = FromContinuedFraction[ ContinuedFraction[ Sqrt[m], n]]; {Numerator[s], Denominator[s]}];
yy = DeleteCases[PellSolve /@ Range[10^5], {}][[All, 2]];
Reap[Module[{y, record = 0}, Sow[0]; For[i = 1, i <= Length@yy, i++, y = yy[[i]]; If[y > record, record = y; Sow[y]]]]][[2, 1]] (* Jean-François Alcover, Nov 21 2020, after N. J. A. Sloane in A002350 *)