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Search: id:A117045
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| A117045 |
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Integers n (not perfect squares) such that the continued fraction expansion of the square root of n has period at most 2. |
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+0
1
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| 2, 3, 5, 6, 8, 10, 11, 15, 17, 18, 20, 24, 26, 27, 30, 35, 37, 38, 39, 40, 42, 48, 50, 51, 56, 63, 65, 66, 68, 72, 80, 82, 83, 84, 87, 90
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In a recent paper Justin Thomas, myself and Julian Rosen show that this is equivalent to the following criterion: let d be the integer part of the square root. Then sqrt{n} has period at most 2 if and only if 2d/(n - d^2) is an integer.
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REFERENCES
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Thomas, J., Shankar, K., Rosen, J., "Continued Fractions, Square Roots and the orbit of 1/0 on the boundary of the hyperbolic plane", preprint.
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LINKS
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K. Shankar, Square roots and continued fractions.
K. Shankar, SQUARE ROOTS, CONTINUED FRACTIONS AND THE ORBIT OF 1/0 ON dH2
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EXAMPLE
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The first term is 2 because sqrt{2} is irrational and for n=2, d=1, 2d/(n - d^2) = 1 is an integer.
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CROSSREFS
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Sequence in context: A135260 A085921 A005243 this_sequence A025055 A080276 A120836
Adjacent sequences: A117042 A117043 A117044 this_sequence A117046 A117047 A117048
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KEYWORD
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nonn
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AUTHOR
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Krishnan Shankar (shankar(AT)math.ou.edu), Apr 17 2006
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