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

1,1

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

Links

Harry J. Smith, Table of n, a(n) for n = 1..20000

Wikipedia, Bretschneider's formula.

Index entries for algebraic numbers, degree 2

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

Example

4.898979485566356196394568149411782783931894961313340256865385134501920....

Mathematica

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

Prog

(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

Crossrefs

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

Cf. A010464, A090654.

Sequence in context: A108616 A200634 A154177 * A087021 A163409 A312828

Adjacent sequences: A010477 A010478 A010479 * A010481 A010482 A010483

Keyword

nonn,cons

Author

N. J. A. Sloane

Extensions

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

Status

approved