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A200991
Decimal expansion of square root of 221/25
2
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
OFFSET
1,1
COMMENTS
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.
REFERENCES
J. H. Conway and R. K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996, p. 187
LINKS
Eric Weisstein's World of Mathematics, Lagrange Number.
FORMULA
With m = 5 being a Markov number (A002559), L = sqrt(9 - 4/m^2).
EXAMPLE
2.9732137494637011045224016...
MATHEMATICA
RealDigits[Sqrt[221/25], 10, 100][[1]]
PROG
(PARI) sqrt(221)/5 \\ Charles R Greathouse IV, Dec 06 2011
CROSSREFS
Cf. A002163 (the first Lagrange number), A010466 (the second Lagrange number).
Sequence in context: A335605 A308320 A254140 * A013500 A244596 A309928
KEYWORD
nonn,cons
AUTHOR
Alonso del Arte, Dec 06 2011
STATUS
approved