A042116 Numerators of continued fraction convergents to sqrt(583).

24, 145, 169, 1328, 6809, 28564, 149629, 1075967, 1225596, 8429543, 405843660, 2443491503, 2849335163, 22388837644, 114793523383, 481562931176, 2522608179263, 18139820186017, 20662428365280, 142114390377697, 6842153166494736, 41195033389346113

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 16859086, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^19 -24*x^18 +145*x^17 -169*x^16 +1328*x^15 -6809*x^14 +28564*x^13 -149629*x^12 +1075967*x^11 -1225596*x^10 -8429543*x^9 -1225596*x^8 -1075967*x^7 -149629*x^6 -28564*x^5 -6809*x^4 -1328*x^3 -169*x^2 -145*x -24) / (x^20 -16859086*x^10 +1). - Colin Barker, Dec 02 2013

Mathematica

Numerator[Convergents[Sqrt[583], 30]] (* Vincenzo Librandi, Nov 17 2013 *)

Crossrefs

Cf. A042117, A040558.

Sequence in context: A129923 A064138 A158047 * A215756 A340639 A290313

Adjacent sequences: A042113 A042114 A042115 * A042117 A042118 A042119

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved