A010464 Decimal expansion of square root of 6.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

Continued fraction expansion is 2 followed by {2, 4} repeated. - Harry J. Smith, Jun 05 2009

Ratio t*o/c^2 where t, o and c are respectively the edge lengths of a tetrahedron, an octahedron and a cube whose total surface areas are the same. See CNRS links. - Michel Marcus, Mar 03 2022 and Apr 21 2016

Diameter of a sphere whose surface area equals 6*Pi. More generally, the square root of x is also the diameter of a sphere whose surface area equals x*Pi. - Omar E. Pol, Aug 29 2024

Examples

			2.449489742783178098197284074705891391965947480656670128432692567250960...
Sqrt(6) = sqrt(1+i*sqrt(3)) + sqrt(1-i*sqrt(3)), where i=sqrt(-1). - _Bruno Berselli_, Nov 20 2012
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Jason Kimberley, Index of expansions of sqrt(d) in base b
• R. J. Nemiroff and J. Bonnell, Plouffe's Inverter, The first 1 million digits of the square root of 6
• R. J. Nemiroff and J. Bonnell, The first 1 million digits of the square root of 6
• Ana Rechtman, Avril 2016, 2e défi, Images des Mathématiques, CNRS, 2016.
• Ana Rechtman, Avril 2016, 3e défi (Solution du 2e défi d’Avril), Images des Mathématiques, CNRS, 2016.
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A002193 (sqrt(2)), A002194 (sqrt(3)).

Cf. A040003 (continued fraction).

Programs

Magma

SetDefaultRealField(RealField(100)); Sqrt(6); // Vincenzo Librandi, Feb 15 2020

Mathematica

RealDigits[N[Sqrt[6],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2011 *)

PARI

default(realprecision, 20080); x=sqrt(6); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010464.txt", n, " ", d));  \\ Harry J. Smith, Jun 01 2009

PARI

sqrt(6) \\ Michel Marcus, Apr 21 2016

Formula

Equals A002193*A002194. - Michel Marcus, Apr 21 2016