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A035015
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Period of continued fraction for square root of n-th squarefree integer.
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3
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1, 2, 1, 2, 4, 1, 2, 5, 4, 2, 1, 6, 6, 6, 4, 1, 5, 2, 8, 4, 4, 2, 1, 2, 2, 3, 2, 10, 12, 4, 2, 5, 4, 6, 7, 6, 11, 4, 1, 2, 10, 8, 6, 8, 7, 5, 6, 4, 4, 1, 2, 5, 10, 2, 5, 8, 10, 16, 4, 11, 1, 2, 12, 2, 9, 6, 15, 2, 6, 9, 6, 10, 10, 4, 1, 2, 12, 10, 3, 6, 16, 14, 9, 4, 18, 4, 4, 2, 1, 2, 9, 20, 10, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| S. R. Finch, Class number theory
R. Knott, An Introduction to Continued Fractions
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EXAMPLE
| a(1)=1 because 2 is smallest squarefree integer and sqrt 2 = [ 1,2,2,2,2... ] thus has an eventual period of 1.
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MATHEMATICA
| Length[ContinuedFraction[Sqrt[#]][[2]]]&/@Select[ Range[ 2, 200], SquareFreeQ] (* From Harvey P. Dale, Jul 17 2011 *)
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CROSSREFS
| Cf. A003285, A013943.
Sequence in context: A138882 A074634 A152036 * A203647 A114791 A129994
Adjacent sequences: A035012 A035013 A035014 * A035016 A035017 A035018
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KEYWORD
| nonn,easy,nice
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AUTHOR
| David L. Treumann (alewifepurswest(AT)yahoo.com)
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EXTENSIONS
| Corrected and extended by James A. Sellers (sellersj(AT)math.psu.edu)
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