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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

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

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 *)

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

Cf. A041318, A010217, A041019, A041047, A041091, A041151, A041227, A041319, A041427 and A041551.

Sequence in context: A041072 A154741 A041999 * A042315 A288667 A319487

Adjacent sequences:  A041316 A041317 A041318 * A041320 A041321 A041322

KEYWORD

nonn,easy,frac

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)