A289091 Decimal expansion of (E(|x|^5))^(1/5), with x being a normally distributed random variable.

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

Offset

1,2

Comments

The 5th root r(5) of the expected value E(|x|^5) for a normal distribution with zero mean and standard deviation 1. See A289090 for more details.

Links

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

Wikipedia, Normal distribution.

Formula

Equals r(5), where r(p) = ((p-1)!!*sqrt(2/Pi))^(1/p).

Equals (8*A076668)^(1/5).

Example

1.44879190154930528525354659881281058821340103935196780729503058015...

Mathematica

RealDigits[(8*Sqrt[2/Pi])^(1/5), 10, 120][[1]] (* Amiram Eldar, Mar 22 2026 *)

Prog

(PARI) \\ General code, for any p > 0:
r(p) = (sqrt(2/Pi)^(p%2)*prod(k=0, (p-2)\2, p-1-2*k))^(1/p);
a = r(5) \\ Present instance

Crossrefs

Cf. A060294, A076668 (p=1), A289090 (p=3), A011002 (p=4), A011350 (p=6).

Sequence in context: A110648 A390378 A198936 * A019674 A264606 A388438

Adjacent sequences: A289088 A289089 A289090 * A289092 A289093 A289094

Keyword

nonn,cons

Author

Stanislav Sykora, Jul 26 2017

Status

approved