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

1,1

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

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.

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

Example

7.745966692414833770358530799564799221665843410583181653175147532226966....

Mathematica

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

Prog

(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

Crossrefs

Cf. A040052 (continued fraction).

Cf. A010472, A011053, A020772, A020817.

Sequence in context: A086315 A185577 A201517 * A225402 A375190 A081824

Adjacent sequences: A010510 A010511 A010512 * A010514 A010515 A010516

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved