A145331 Numbers X such that there exists Y in N : X^2=129*Y^2+43.

602, 20292818, 684070894178, 23060029822447562, 777353604630636420842, 26204589989038723924136258, 883356727753141778851996836338, 29777955266353819376062089428817722, 1003814871145430523413911255793448572282

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (33710,-1).

Formula

a(n+2) = 33710*a(n+1)-a(n).

G.f.: -602*x*(x-1) / (x^2-33710*x+1). - Colin Barker, Oct 21 2014

Example

a(1)=602 because the first relation is 602^2=129*53^2+43.

Mathematica

CoefficientList[Series[602(1 - x)/(x^2 - 33710 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)

Prog

(PARI) Vec(-602*x*(x-1)/(x^2-33710*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014
(Magma) I:=[602, 20292818]; [n le 2 select I[n] else 33710*Self(n-1)-Self(n-2): n in [1..10]]; // Vincenzo Librandi Oct 21 2014

Crossrefs

Sequence in context: A218650 A218180 A218521 * A252957 A348077 A066785

Adjacent sequences: A145328 A145329 A145330 * A145332 A145333 A145334

Keyword

easy,nonn

Author

Richard Choulet, Oct 08 2008

Extensions

Editing from Colin Barker, Oct 21 2014

Status

approved