The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A041551 Denominators of continued fraction convergents to sqrt(293). 10
 1, 8, 9, 17, 145, 4947, 39721, 44668, 84389, 719780, 24556909, 197175052, 221731961, 418907013, 3572988065, 121900501223, 978776997849, 1100677499072, 2079454496921, 17736313474440, 605114112627881, 4858649214497488, 5463763327125369, 10322412541622857 (list; graph; refs; listen; history; text; internal format)
 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, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 25 11:40 EDT 2023. Contains 365644 sequences. (Running on oeis4.)