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A041091
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Denominators of continued fraction convergents to sqrt(53).
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11
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 12 2010: (Start)
The a(n) 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.
(End)
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FORMULA
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 12 2010: (Start)
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.
(End)
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MATHEMATICA
| Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[53], n]]], {n, 1, 50}] (* From Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *)
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CROSSREFS
| Cf. A041090.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 12 2010: (Start)
Cf. A041019, A041047, A041091, A041151, A041227, A041319, A041427 and A041551.
(End)
Sequence in context: A056655 A145593 A042037 * A117764 A113874 A007677
Adjacent sequences: A041088 A041089 A041090 * A041092 A041093 A041094
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KEYWORD
| nonn,cofr,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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