A272873 Decimal expansion of the quadratic mean of 1 and Pi.

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

Offset

1,1

Comments

Quadratic mean (also known as the root mean square, rms) of two numbers x and y, is the Hoelder mean H(x,y,p) = ((x^2+y^2)/2)^(1/p) with p = 2.

Links

Stanislav Sykora, Table of n, a(n) for n = 1..1000

Wikipedia, Generalized mean

Index entries for transcendental numbers

Formula

Equals sqrt((1+Pi^2)/2).

Example

2.3312662225804841162152530194296857517396337769556644593068408873...

Mathematica

RealDigits[Sqrt[(1+Pi^2)/2], 10, 120][[1]] (* Harvey P. Dale, Apr 01 2018 *)

Prog

(PARI) sqrt((1+Pi^2)/2)

Crossrefs

Cf. A000796, A002388.

Other means of 1 and Pi: A002161 (geometric, p=0), A191502 (AGM), A197733 (harmonic, p=-1), A269430 (arithmetic, p=1).

Sequence in context: A051911 A106595 A181608 * A295634 A317665 A329315

Adjacent sequences: A272870 A272871 A272872 * A272874 A272875 A272876

Keyword

nonn,cons

Author

Stanislav Sykora, May 15 2016

Status

approved