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A041046
Numerators of continued fraction convergents to sqrt(29).
11
5, 11, 16, 27, 70, 727, 1524, 2251, 3775, 9801, 101785, 213371, 315156, 528527, 1372210, 14250627, 29873464, 44124091, 73997555, 192119201, 1995189565, 4182498331, 6177687896, 10360186227, 26898060350
OFFSET
0,1
COMMENTS
From Johannes W. Meijer, Jun 12 2010: (Start)
The terms of this sequence can be constructed with the terms of sequence A087130.
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. (End)
LINKS
FORMULA
a(5*n) = A087130(3*n+1), a(5*n+1) = (A087130(3*n+2) - A087130(3*n+1))/2, a(5*n+2) = ( A087130(3*n+2) + A087130(3*n+1))/2, a(5*n+3) = A087130(3*n+2) and a(5*n+4) = A087130(3*n+3)/2. - Johannes W. Meijer, Jun 12 2010
G.f.: (5 + 11*x + 16*x^2 + 27*x^3 + 70*x^4 + 27*x^5 - 16*x^6 + 11*x^7 - 5*x^8 + x^9)/(1 - 140*x^5 - x^10) - Peter J. C. Moses, Jul 29 2013
MATHEMATICA
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[29], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)
Numerator[Convergents[Sqrt[29], 30]] (* Vincenzo Librandi, Oct 28 2013 *)
LinearRecurrence[ {0, 0, 0, 0, 140, 0, 0, 0, 0, 1}, {5, 11, 16, 27, 70, 727, 1524, 2251, 3775, 9801}, 30] (* Harvey P. Dale, Jun 10 2021 *)
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved