A041551 Denominators of continued fraction convergents to sqrt(293).

1, 8, 9, 17, 145, 4947, 39721, 44668, 84389, 719780, 24556909, 197175052, 221731961, 418907013, 3572988065, 121900501223, 978776997849, 1100677499072, 2079454496921, 17736313474440, 605114112627881, 4858649214497488, 5463763327125369, 10322412541622857

Offset

0,2

Comments

The a(n) terms of this sequence can be constructed with the terms of sequence A178765. For the terms of the periodical sequence of the continued fraction for sqrt(293) see A040275. We observe that its period is five. - Johannes W. Meijer, Jun 12 2010

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, 4964, 0, 0, 0, 0, 1).

Formula

a(5n) = A178765(3n), a(5n+1) = (A178765(3n+1) - A178765(3n))/2, a(5n+2) = (A178765(3n+1) + A178765(3n))/2, a(5n+3) = A178765(3n+1) and a(5n+4) = A178765(3n+2)/2. - Johannes W. Meijer, Jun 12 2010

G.f.: -(x^8-8*x^7+9*x^6-17*x^5+145*x^4+17*x^3+9*x^2+8*x+1) / (x^10+4964*x^5-1). - Colin Barker, Nov 12 2013

a(n) = 4964*a(n-5) + a(n-10) for n>9. - Vincenzo Librandi, Dec 20 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[293], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *)
Denominator[Convergents[Sqrt[293 ], 30]] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 8, 9, 17, 145, 4947, 39721, 44668, 84389, 719780]; [n le 10 select I[n] else 4964*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041550, A040275, A041019, A041047, A041091, A041151, A041227, A041319, A041427 and A041551.

Sequence in context: A042753 A042727 A041128 * A356699 A057104 A359062

Adjacent sequences: A041548 A041549 A041550 * A041552 A041553 A041554

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved