A020784 Decimal expansion of 1/sqrt(27).

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

Comments

This is the minimum ripple factor for a third-order Chebyshev filter for which the generalized reflectionless topology needs no negative elements. - Matthew A. Morgan, Oct 18 2017

Examples

			0.1924500897298752548363829268339858185492005837567089586728674....
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Sections 8.4.3 and 8.16, pp. 495, 527.

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A002194, A010482, A020760, A021031, A073010, A212886.

Programs

Magma

1/Sqrt(27); // G. C. Greubel, Feb 15 2018

Mathematica

RealDigits[1/Sqrt[27],10,200][[1]] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)
realDigitsRecip[Sqrt[27]] (* The realDigitsRecip program is at A021200 *) (* Harvey P. Dale, Jul 05 2025 *)

PARI

1/sqrt(27) \\ G. C. Greubel, Feb 15 2018

Formula

Equals Sum_{k>=0} binomial(2*k,k) * k/16^k. - Amiram Eldar, Aug 02 2020

Equals sqrt(3)/9. - Stefano Spezia, Dec 24 2024

Equals 1/A010482 = A020760/3 = sqrt(A021031) = A073010/Pi = A212886/2. - Hugo Pfoertner, Dec 24 2024