A041146 Numerators of continued fraction convergents to sqrt(83).

9, 82, 1485, 13447, 243531, 2205226, 39937599, 361643617, 6549522705, 59307347962, 1074081786021, 9726043422151, 176142863384739, 1595011813884802, 28886355513311175, 261572211433685377, 4737186161319647961, 42896247663310517026, 776869644100908954429

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..70
• Index entries for linear recurrences with constant coefficients, signature (0,164,0,-1).

Crossrefs

Cf. A010534, A041147.

Programs

Mathematica

Numerator[Convergents[Sqrt[83], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0,164,0,-1},{9,82,1485,13447},20] (* Harvey P. Dale, Apr 12 2022 *)

Formula

G.f.: -(x^3-9*x^2-82*x-9) / (x^4-164*x^2+1). - Colin Barker, Nov 05 2013

Extensions

More terms from Colin Barker, Nov 05 2013