This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A200991 #44 Jun 02 2025 07:20:08 %S A200991 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, %T A200991 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, %U A200991 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 %N A200991 Decimal expansion of square root of 221/25. %C A200991 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. %C A200991 Continued fraction is 2 followed by 1, 36, 3, 148, 3, 36, 1, 4 repeated. %D A200991 J. H. Conway and R. K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996, p. 187 %H A200991 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LagrangeNumber.html">Lagrange Number</a>. %F A200991 With m = 5 being a Markov number (A002559), L = sqrt(9 - 4/m^2). %e A200991 2.9732137494637011045224016... %t A200991 RealDigits[Sqrt[221/25], 10, 100][[1]] %o A200991 (PARI) sqrt(221)/5 \\ _Charles R Greathouse IV_, Dec 06 2011 %Y A200991 Cf. A002163 (the first Lagrange number), A010466 (the second Lagrange number). %K A200991 nonn,cons %O A200991 1,1 %A A200991 _Alonso del Arte_, Dec 06 2011