%I #29 Oct 02 2024 10:53:04
%S 7,7,4,5,9,6,6,6,9,2,4,1,4,8,3,3,7,7,0,3,5,8,5,3,0,7,9,9,5,6,4,7,9,9,
%T 2,2,1,6,6,5,8,4,3,4,1,0,5,8,3,1,8,1,6,5,3,1,7,5,1,4,7,5,3,2,2,2,6,9,
%U 6,6,1,8,3,8,7,3,9,5,8,0,6,7,0,3,8,5,7,4,7,5,3,7,1,7,3,4,7,0,3
%N Decimal expansion of square root of 60.
%C Continued fraction expansion is 7 followed by {1, 2, 1, 14} repeated. - _Harry J. Smith_, Jun 07 2009
%C With a different offset, decimal expansion of 0.6. In a unimodal distribution, the mean and median differ by at most 0.6 standard deviations (and this is sharp), see Basu & DasGupta. - _Charles R Greathouse IV_, Oct 01 2024
%H Harry J. Smith, <a href="/A010513/b010513.txt">Table of n, a(n) for n = 1..20000</a>
%H Sanjib Basu and Anirban DasGupta, <a href="https://doi.org/10.1137/S0040585X97975447">The Mean, Median, and Mode of Unimodal Distributions: A Characterization</a>, Theory of Probability & Its Applications 41:2 (1997), pp. 210-223; <a href="https://www.stat.purdue.edu/docs/research/tech-reports/1992/tr92-40.pdf">alternative link</a>.
%F Equals 10 * sqrt(3/5) = 10 * Sum_{k>=0} (-1)^k * binomial(2*k,k)/6^k. - _Amiram Eldar_, Aug 03 2020
%F Equals 2*A010472 = A011053^2 = 30*A020772 = 1/A020817. - _Hugo Pfoertner_, Oct 02 2024
%e 7.745966692414833770358530799564799221665843410583181653175147532226966....
%t RealDigits[N[Sqrt[60],200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 25 2011 *)
%o (PARI) { default(realprecision, 20080); x=sqrt(60); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010513.txt", n, " ", d)); } \\ _Harry J. Smith_, Jun 07 2009
%Y Cf. A040052 (continued fraction).
%Y Cf. A010472, A011053, A020772, A020817.
%K nonn,cons
%O 1,1
%A _N. J. A. Sloane_