A010464 - OEIS

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

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

FORMULA

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

EXAMPLE

2.449489742783178098197284074705891391965947480656670128432692567250960...

Sqrt(6) = sqrt(1+i*sqrt(3)) + sqrt(1-i*sqrt(3)), where i=sqrt(-1). - Bruno Berselli, Nov 20 2012

MATHEMATICA

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

PROG

(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

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

CROSSREFS

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

Cf. A040003 (continued fraction).

Sequence in context: A281122 A201777 A096189 * A187209 A006579 A227906

Adjacent sequences: A010461 A010462 A010463 * A010465 A010466 A010467

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

STATUS

approved