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Search: id:A013645
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| A013645 |
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Values of n at which period of continued fraction for sqrt(n) increases. |
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3
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| 1, 2, 3, 7, 13, 19, 31, 43, 46, 94, 139, 151, 166, 211, 331, 421, 526, 571, 604, 631, 751, 886, 919, 1291, 1324, 1366, 1516, 1621, 1726, 2011, 2311, 2566, 2671, 3004, 3019, 3334, 3691, 3931, 4174, 4846, 5119, 6211, 6451, 6679, 6694, 7606, 8254, 8779, 8941, 9739
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 426 (but beware of errors!).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
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EXAMPLE
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The continued fraction for Sqrt(31) is 5, {1, 1, 3, 5, 3, 1, 1, 10}, and the continued fraction for Sqrt(43) is 6, {1, 1, 3, 1, 5, 1, 3, 1, 1, 12}; and there is no number between 31 and 43 whose square root produces a continued fraction the period of which exceeds the one for 31.
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MATHEMATICA
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a = -1; Do[l = Length[ Last[ ContinuedFraction[ Sqrt[ n]]]]; If[ l > a, a = l; Print[n]], {n, 1, 10^4} ]
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CROSSREFS
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Cf. A003285.
Sequence in context: A101415 A045331 A053613 this_sequence A130272 A038940 A019383
Adjacent sequences: A013642 A013643 A013644 this_sequence A013646 A013647 A013648
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KEYWORD
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nonn,nice
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net)
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