A040003 -id:A040003 - cp's OEIS frontend

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

N. J. A. Sloane

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

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

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

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

Cf. A040003 (continued fraction).

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

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

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
```

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

A382713 Simple continued fraction expansion of sqrt(3/2).

Original entry on oeis.org

1, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2

Offset: 0

N. J. A. Sloane, Apr 08 2025

Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A105397, A115754, A142238, A142239.

Essentially the same as A106469, A040003, A010694.

with(numtheory); cfrac (sqrt(3/2, 70, 'quotients');

PadRight[{1}, 100, {2, 4}] (* Paolo Xausa, Apr 14 2025 *)

def A382713(n): return 1<<1+(n&1) if n else 1 # Chai Wah Wu, Apr 09 2025

A004564 Expansion of sqrt(6) in base 5.

Original entry on oeis.org

2, 2, 1, 1, 0, 4, 3, 1, 1, 4, 3, 1, 1, 3, 3, 1, 3, 4, 1, 2, 1, 4, 1, 1, 2, 1, 2, 4, 4, 3, 0, 1, 4, 1, 3, 0, 1, 0, 4, 4, 0, 3, 3, 1, 1, 1, 4, 3, 0, 0, 0, 0, 0, 3, 1, 2, 2, 0, 4, 1, 1, 2, 0, 0, 2, 3, 1, 4, 1, 0, 3, 1, 3, 3, 3, 0, 1, 2, 3, 0, 3, 1, 4, 1, 0, 0, 3, 2, 2, 0, 0, 0, 0, 3, 3, 2, 3, 2, 3

Offset: 1

N. J. A. Sloane

			In base 5: sqrt(11) = 2.21104311431133134121411...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Jason Kimberley, Index of expansions of sqrt(d) in base b

Cf. A040003, A010464.

d:= 6; m:=5; Prune(Reverse(IntegerToSequence(Isqrt(d*m^100), m))); // G. C. Greubel, Mar 26 2018

RealDigits[Sqrt[6], 5, 100][[1]] (* Alonso del Arte, Aug 27 2012 *)

Updated by Alois P. Heinz at the suggestion of Kevin Ryde, Feb 19 2012

A064851 Period of continued fraction for sqrt(6)*n.

Original entry on oeis.org

2, 2, 6, 4, 2, 6, 6, 8, 2, 2, 4, 12, 16, 6, 12, 12, 22, 2, 18, 2, 24, 4, 20, 20, 18, 12, 10, 8, 22, 8, 26, 32, 4, 14, 8, 8, 40, 10, 40, 4, 34, 16, 38, 8, 8, 16, 40, 44, 2, 14, 10, 24, 50, 10, 12, 4, 18, 22, 22, 8, 56, 26, 20, 60, 32, 4, 58, 24, 60, 4, 68, 20, 34, 40, 58, 24, 28, 44

Offset: 1

R. K. Guy, Oct 26 2001

nonn

			A040003 (cfrac for n=1) has period length 2, so a(1)=2. A040019 (cfrac for n=2) has period length 2, so a(2)=2. A010140 (cfrac for n=3) has period length 6, so a(3)=6. - _R. J. Mathar_, Feb 10 2016

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A010464 Decimal expansion of square root of 6.

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A382713 Simple continued fraction expansion of sqrt(3/2).

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A004564 Expansion of sqrt(6) in base 5.

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A064851 Period of continued fraction for sqrt(6)*n.

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