A158365 529n - 1.

528, 1057, 1586, 2115, 2644, 3173, 3702, 4231, 4760, 5289, 5818, 6347, 6876, 7405, 7934, 8463, 8992, 9521, 10050, 10579, 11108, 11637, 12166, 12695, 13224, 13753, 14282, 14811, 15340, 15869, 16398, 16927, 17456, 17985, 18514, 19043, 19572

Offset

1,1

Comments

The identity (529*n-1)^2-(529*n^2-2*n)*(23)^2=1 can be written as a(n)^2-A158364(n)*(23)^2=1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(23^2*t-2)).

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 2*a(n-1)-a(n-2).

G.f.: x*(528+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {528, 1057}, 50]
529*Range[40]-1 (* Harvey P. Dale, Jul 08 2017 *)

Prog

(Magma) I:=[528, 1057]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 529*n - 1.

Crossrefs

Cf. A158364.

Sequence in context: A232885 A085329 A157475 * A076580 A304512 A037944

Adjacent sequences: A158362 A158363 A158364 * A158366 A158367 A158368

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2009

Status

approved