A158386 a(n) = 676*n + 1.

677, 1353, 2029, 2705, 3381, 4057, 4733, 5409, 6085, 6761, 7437, 8113, 8789, 9465, 10141, 10817, 11493, 12169, 12845, 13521, 14197, 14873, 15549, 16225, 16901, 17577, 18253, 18929, 19605, 20281, 20957, 21633, 22309, 22985, 23661, 24337

Offset

1,1

Comments

The identity (676*n+1)^2-(676*n^2+2*n)*(26)^2=1 can be written as a(n)^2-A158385(n)*(26)^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*(26^2*t+2)).

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

Formula

G.f.: x*(677-x)/(1-x)^2.

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

Mathematica

LinearRecurrence[{2, -1}, {677, 1353}, 50]
676*Range[40]+1 (* Harvey P. Dale, Feb 07 2023 *)

Prog

(Magma) I:=[677, 1353]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 676*n + 1.

Crossrefs

Cf. A158385.

Sequence in context: A058450 A159893 A142755 * A031730 A205749 A108824

Adjacent sequences: A158383 A158384 A158385 * A158387 A158388 A158389

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2009

Status

approved