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A041019
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Denominators of continued fraction convergents to sqrt(13).
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10
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1, 1, 2, 3, 5, 33, 38, 71, 109, 180, 1189, 1369, 2558, 3927, 6485, 42837, 49322, 92159, 141481, 233640, 1543321, 1776961, 3320282, 5097243, 8417525, 55602393, 64019918, 119622311, 183642229, 303264540
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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 A006190.
For the terms of the periodical sequence of the continued fraction for sqrt(13) see A010122. We observe that its period is five. The decimal expansion of sqrt(13) is A010470.
(End)
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FORMULA
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 12 2010: (Start)
a(5*n) = A006190(3*n+1), a(5*n+1) = (A006190(3*n+2) - A006190(3*n+1))/2, a(5*n+2) = (A006190(3*n+2) + A006190(3*n+1))/2, a(5*n+3) = A006190(3*n+2) and a(5*n+4) = A006190(3*n+3)/2.
(End)
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MATHEMATICA
| Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[13], n]]], {n, 1, 50}] (*From Vladimir Joseph Stephan Orlovsky, Mar 16 2011*)
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CROSSREFS
| Cf. A041018.
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: A036797 A163079 A109845 * A041977 A089213 A029499
Adjacent sequences: A041016 A041017 A041018 * A041020 A041021 A041022
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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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