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 A041091 Denominators of continued fraction convergents to sqrt(53). 11
 1, 3, 4, 7, 25, 357, 1096, 1453, 2549, 9100, 129949, 398947, 528896, 927843, 3312425, 47301793, 145217804, 192519597, 337737401, 1205731800, 17217982601, 52859679603, 70077662204, 122937341807, 438889687625, 6267392968557, 19241068593296, 25508461561853 (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 A054413. For the terms of the periodic sequence of the continued fraction for sqrt(53) see A010139. We observe that its period is five. The decimal expansion of sqrt(53) is A010506. - 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 (0,0,0,0,364,0,0,0,0,1). FORMULA a(5*n) = A054413(3*n), a(5*n+1) = (A054413(3*n+1) - A054413(3*n))/2, a(5*n+2)= (A054413(3*n+1) + A054413(3*n))/2, a(5*n+3) = A054413(3*n+1) and a(5*n+4) = A054413(3*n+2)/2. - Johannes W. Meijer, Jun 12 2010 G.f.: -(x^8-3*x^7+4*x^6-7*x^5+25*x^4+7*x^3+4*x^2+3*x+1) / (x^10+364*x^5-1). - Colin Barker, Sep 26 2013 MAPLE convert(sqrt(53), confrac, 30, cvgts): denom(cvgts); # Wesley Ivan Hurt, Dec 17 2013 MATHEMATICA Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[53], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *) Denominator[Convergents[Sqrt[53], 30]] (* Vincenzo Librandi, Oct 24 2013 *) LinearRecurrence[{0, 0, 0, 0, 364, 0, 0, 0, 0, 1}, {1, 3, 4, 7, 25, 357, 1096, 1453, 2549, 9100}, 30] (* Harvey P. Dale, Nov 13 2019 *) CROSSREFS Cf. A010506, A041090. Cf. A041019, A041047, A041151, A041227, A041319, A041427 and A041551. - Johannes W. Meijer, Jun 12 2010 Sequence in context: A288049 A145593 A042037 * A270373 A117764 A113874 Adjacent sequences: A041088 A041089 A041090 * A041092 A041093 A041094 KEYWORD nonn,frac,easy AUTHOR N. J. A. Sloane. STATUS approved

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Last modified July 23 14:20 EDT 2024. Contains 374549 sequences. (Running on oeis4.)