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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
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
Sequence in context: A288049 A145593 A042037 * A270373 A117764 A113874
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved

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