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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 periodical 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 December 16 04:05 EST 2019. Contains 330013 sequences. (Running on oeis4.)