login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041319 Denominators of continued fraction convergents to sqrt(173). 10
1, 6, 7, 13, 85, 2223, 13423, 15646, 29069, 190060, 4970629, 30013834, 34984463, 64998297, 424974245, 11114328667, 67110946247, 78225274914, 145336221161, 950242601880, 24851643870041, 150060105822126, 174911749692167, 324971855514293, 2124742882777925 (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 A140455. For the terms of the periodical sequence of the continued fraction for sqrt(173) see A010217. We observe that its period is five. - Johannes W. Meijer, Jun 12 2010
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 2236, 0, 0, 0, 0, 1).
FORMULA
a(5*n) = A140455(3*n+1), a(5*n+1) = (A140455(3*n+2) - A140455(3*n+1))/2, a(5*n+2) = (A140455(3*n+2)+A140455(3*n+1))/2, a(5*n+3) = A140455(3*n+2) and a(5*n+4) = A140455(3*n+3)/2. - Johannes W. Meijer, Jun 12 2010
G.f.: -(x^8-6*x^7+7*x^6-13*x^5+85*x^4+13*x^3+7*x^2+6*x+1) / (x^10+2236*x^5-1). - Colin Barker, Nov 12 2013
a(n) = 2236*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 15 2013
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[173], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *)
Denominator[Convergents[Sqrt[173], 30]] (* Vincenzo Librandi, Dec 15 2013 *)
LinearRecurrence[{0, 0, 0, 0, 2236, 0, 0, 0, 0, 1}, {1, 6, 7, 13, 85, 2223, 13423, 15646, 29069, 190060}, 30] (* Harvey P. Dale, Sep 19 2020 *)
PROG
(Magma) I:=[1, 6, 7, 13, 85, 2223, 13423, 15646, 29069, 190060]; [n le 10 select I[n] else 2236*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013
CROSSREFS
Sequence in context: A041072 A154741 A041999 * A042315 A288667 A319487
KEYWORD
nonn,easy,frac
AUTHOR
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)