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 A041047 Denominators of continued fraction convergents to sqrt(29). 11
 1, 2, 3, 5, 13, 135, 283, 418, 701, 1820, 18901, 39622, 58523, 98145, 254813, 2646275, 5547363, 8193638, 13741001, 35675640, 370497401, 776670442, 1147167843, 1923838285, 4994844413, 51872282415 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The terms of this sequence can be constructed with the terms of sequence A052918. For the terms of the periodical sequence of the continued fraction for sqrt(29) see A010128. We observe that its period is five. The decimal expansion of sqrt(29) is A010484. - 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 (0,0,0,0,140,0,0,0,0,1). FORMULA a(5*n) = A052918(3*n), a(5*n+1) = (A052918(3*n+1) - A052918(3*n))/2, a(5*n+2) = (A052918(3*n+1) + A052918(3*n))/2, a(5*n+3) = A052918(3*n+1) and a(5*n+4) = A052918(3*n+2)/2. - Johannes W. Meijer, Jun 12 2010 G.f.: (1 + 2*x + 3*x^2 + 5*x^3 + 13*x^4 - 5*x^5 + 3*x^6 - 2*x^7 + x^8)/(1 - 140*x^5 - x^10). - Peter J. C. Moses, Jul 29 2013 a(n) = 140*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 10 2013 MATHEMATICA Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[29], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *) Denominator[Convergents[Sqrt[29], 30]] (* Vincenzo Librandi, Dec 10 2013 *) PROG (Magma) I:=[1, 2, 3, 5, 13, 135, 283, 418, 701, 1820]; [n le 10 select I[n] else 140*Self(n-5)+Self(n-10): n in [1..50]]; // Vincenzo Librandi, Dec 10 2013 CROSSREFS Cf. A041046. Cf. A041019, A041047, A041091, A041151, A041227, A041319, A041427, A041551. Sequence in context: A139095 A005478 A117740 * A120494 A038601 A372228 Adjacent sequences: A041044 A041045 A041046 * A041048 A041049 A041050 KEYWORD nonn,cofr,frac,easy AUTHOR N. J. A. Sloane. STATUS approved

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Last modified May 18 08:25 EDT 2024. Contains 372618 sequences. (Running on oeis4.)