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A200991
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Decimal expansion of square root of 221/25
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2
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2, 9, 7, 3, 2, 1, 3, 7, 4, 9, 4, 6, 3, 7, 0, 1, 1, 0, 4, 5, 2, 2, 4, 0, 1, 6, 4, 2, 7, 8, 6, 2, 7, 9, 3, 3, 0, 2, 8, 9, 7, 9, 7, 1, 0, 2, 7, 4, 4, 1, 7, 2, 3, 1, 2, 1, 1, 2, 6, 1, 8, 9, 6, 2, 0, 5, 0, 3, 6, 7, 4, 6, 2, 9, 5, 6, 2, 3, 3, 5, 3, 1, 7, 2, 3, 1, 6, 7, 2, 9, 2, 0, 5, 4, 7, 9
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OFFSET
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1,1
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COMMENTS
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This is the third Lagrange number, corresponding to the third Markov number (5). With multiples of the golden ration and sqrt(2) excluded from consideration, the Hurwitz irrational number theorem uses this Lagrange number to obtain very good rational approximations for irrational numbers.
Continued fraction is 2 followed by 1, 36, 3, 148, 3, 36, 1, 4 repeated.
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REFERENCES
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J. H. Conway and R. K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996, p. 187
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LINKS
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Table of n, a(n) for n=1..96.
Weisstein, Eric W. "Lagrange Number." From MathWorld--A Wolfram Web Resource.
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FORMULA
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With m = 5 being a Markov number (A002559), L = sqrt(9 - 4/m^2).
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EXAMPLE
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2.973213749463701104522402...
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MATHEMATICA
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RealDigits[Sqrt[221/25], 10, 100][[1]]
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PROG
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(PARI) sqrt(221)/5 \\ Charles R Greathouse IV, Dec 06 2011
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CROSSREFS
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Cf. A002163, the first Lagrange number; A010466, the second Lagrange number.
Sequence in context: A011070 A230480 A254140 * A013500 A244596 A176977
Adjacent sequences: A200988 A200989 A200990 * A200992 A200993 A200994
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KEYWORD
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nonn,cons
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AUTHOR
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Alonso del Arte, Dec 06 2011
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STATUS
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approved
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