A174762 x-values in the solution x^2-61*y^2=1.

1, 1766319049, 6239765965720528801, 22042834973108102061352541449, 77869358613928486808166555366140995201, 275084262906388245923976756042747916825335226249, 971773147303355325052564141449134520779147876502526039201

Offset

1,2

Comments

The corresponding values of y of this Pell equation are in A176364.

The next term has 67 digits. [From Harvey P. Dale, Jan. 15, 2011]

References

Edward J. Barbeau, Pell's Equation (Springer-Verlag 2003) at pp. 23-24.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..100

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

N. J. Wildberger, Pell's equation without irrational numbers, J. Int. Seq. 13 (2010), 10.4.3, Section 7.

Index entries for linear recurrences with constant coefficients, signature (3532638098,-1).

Formula

a(n) = 3532638098*a(n-1)-a(n-2) with a(1)=1, a(2)=1766319049.

G.f.: x*(1-1766319049*x)/(1-3532638098*x+x^2).

Mathematica

LinearRecurrence[{3532638098, -1}, {1, 1766319049}, 20]

Prog

(Magma) I:=[1, 1766319049]; [n le 2 select I[n] else 3532638098*Self(n-1)-Self(n-2): n in [1..10]];

Crossrefs

Cf. A176364.

Sequence in context: A034649 A211240 A258423 * A147769 A198177 A129616

Adjacent sequences: A174759 A174760 A174761 * A174763 A174764 A174765

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 13 2010

Status

approved