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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 (list; constant; graph; refs; listen; history; text; internal format)
 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 Adjacent sequences:  A200988 A200989 A200990 * A200992 A200993 A200994 KEYWORD nonn,cons AUTHOR Alonso del Arte, Dec 06 2011 STATUS approved

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Last modified September 26 17:30 EDT 2021. Contains 347670 sequences. (Running on oeis4.)