A010480 Decimal expansion of square root of 24.

4, 8, 9, 8, 9, 7, 9, 4, 8, 5, 5, 6, 6, 3, 5, 6, 1, 9, 6, 3, 9, 4, 5, 6, 8, 1, 4, 9, 4, 1, 1, 7, 8, 2, 7, 8, 3, 9, 3, 1, 8, 9, 4, 9, 6, 1, 3, 1, 3, 3, 4, 0, 2, 5, 6, 8, 6, 5, 3, 8, 5, 1, 3, 4, 5, 0, 1, 9, 2, 0, 7, 5, 4, 9, 1, 4, 6, 3, 0, 0, 5, 3, 0, 7, 9, 7, 1, 8, 8, 6, 6, 2, 0, 9, 2, 8, 0, 4, 6, 9, 6, 3, 7, 1, 8

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

Continued fraction expansion is 4 followed by {1, 8} repeated. - Harry J. Smith, Jun 03 2009

The solution to the Lane-Emden equation for a sphere of polytropic index n = 0. - Arkadiusz Wesolowski, Nov 11 2014

Using Bretschneider's formula this is the maximum area of a quadrilateral with side lengths of 1,2,3 and 4. - Scott R. Shannon, Jan 06 2020

Examples

			4.898979485566356196394568149411782783931894961313340256865385134501920....
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Wikipedia, Bretschneider's formula.
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A040019 (continued fraction). - Harry J. Smith, Jun 03 2009

Cf. A010464, A090654.

Programs

Mathematica

RealDigits[N[Sqrt[24],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 22 2011 *)

PARI

default(realprecision, 20080); x=sqrt(24); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010480.txt", n, " ", d));  \\ Harry J. Smith, Jun 03 2009

Formula

Equals 2*A010464. - R. J. Mathar, Jan 14 2021

Equals 4 + Sum_{k>=0} (-1)^k * binomial(2*k,k)/((k+1) * 8^k). - Amiram Eldar, May 06 2022

Extensions

Final digits of sequence corrected using the b-file. - N. J. A. Sloane, Aug 30 2009