A175633 Numbers x such that x^2 - 28*y^2 = 1 for some integer y.

1, 127, 32257, 8193151, 2081028097, 528572943487, 134255446617601, 34100354867927167, 8661355881006882817, 2199950293420880308351, 558778713173022591438337, 141927593195654317345029247, 36049049892983023583045990401, 9156316745224492335776336532607, 2325668404237128070263606433291777

Offset

1,2

Comments

This sequence gives the values of x in solutions of the Pell equation x^2 - 28*y^2 = 1; the corresponding y values are in A175672. [Edited by Jon E. Schoenfield, May 04 2014]

Links

Paolo Xausa, Table of n, a(n) for n = 1..416

Index entries for linear recurrences with constant coefficients, signature (254,-1).

Formula

a(n) = 254*a(n-1) - a(n-2) (with a(1)=1, a(2)=127).

G.f.: x*(1-127*x)/(1-254*x+x^2). - Bruno Berselli, Apr 18 2011

Mathematica

LinearRecurrence[{254, -1}, {1, 127}, 15] (* Paolo Xausa, Jul 21 2026 *)

Prog

(PARI) a(n)=([0, 1; -1, 254]^(n-1)*[1; 127])[1, 1] \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Cf. A175672.

Row 8 of array A188644.

Sequence in context: A069408 A289474 A069434 * A175825 A217914 A203798

Adjacent sequences: A175630 A175631 A175632 * A175634 A175635 A175636

Keyword

nonn,easy,changed

Author

Vincenzo Librandi, Dec 04 2010

Extensions

More terms from Paolo Xausa, Jul 21 2026

Status

approved