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A041018
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Numerators of continued fraction convergents to sqrt(13).
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10
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3, 4, 7, 11, 18, 119, 137, 256, 393, 649, 4287, 4936, 9223, 14159, 23382, 154451, 177833, 332284, 510117, 842401, 5564523, 6406924, 11971447, 18378371, 30349818, 200477279, 230827097, 431304376, 662131473
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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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 A006497.
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) = A006497(3*n+1), a(5*n+1) = (A006497(3*n+2)-A006497(3*n+1))/2, a(5*n+2) = (A006497(3*n+2)+A006497(3*n+1))/2, a(5*n+3) = A006497(3*n+2) and a(5*n+4) = A006497(3*n+3)/2.
(End)
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MATHEMATICA
| Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[13], n]]], {n, 1, 50}] (*From Vladimir Joseph Stephan Orlovsky, Mar 16 2011*)
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CROSSREFS
| Cf. A041019. A041018, A041046, A041090, A041150, A041226, A041318, A041426 and A041550.
Sequence in context: A041209 A041739 A042593 * A072255 A049863 A025068
Adjacent sequences: A041015 A041016 A041017 * A041019 A041020 A041021
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KEYWORD
| nonn,frac,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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