A010513 Decimal expansion of square root of 60.

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, 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, 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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

Continued fraction expansion is 7 followed by {1, 2, 1, 14} repeated. - Harry J. Smith, Jun 07 2009

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

Examples

			7.745966692414833770358530799564799221665843410583181653175147532226966....
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Sanjib Basu and Anirban DasGupta, The Mean, Median, and Mode of Unimodal Distributions: A Characterization, Theory of Probability & Its Applications 41:2 (1997), pp. 210-223; alternative link.
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A040052 (continued fraction).

Cf. A010472, A011053, A020772, A020817.

Programs

Mathematica

RealDigits[N[Sqrt[60],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 25 2011 *)

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

Formula

Equals 10 * sqrt(3/5) = 10 * Sum_{k>=0} (-1)^k * binomial(2*k,k)/6^k. - Amiram Eldar, Aug 03 2020

Equals 2*A010472 = A011053^2 = 30*A020772 = 1/A020817. - Hugo Pfoertner, Oct 02 2024