A289090 -id:A289090 - cp's OEIS frontend

A011002 Decimal expansion of 4th root of 3.

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

Offset: 1

N. J. A. Sloane

Also 8th root of 9. - Alonso del Arte, Dec 06 2011

The 4th root r(4) of the expected value E(x^4) for a normal distribution with zero mean and standard deviation 1. See A289090 for more details. - Stanislav Sykora, Jul 26 2017

			1.3160740129524924608192189...

Vincenzo Librandi, Table of n, a(n) for n = 1..5000
Index entries for algebraic numbers, degree 4

Cf. A179615, continued fraction.

Cf. A076668, A011350, A289090, A289091.

Mathematica
```
RealDigits[3^(1/4), 10, 100][[1]]
```

sqrtn(3,4) \\ Charles R Greathouse IV, Apr 14 2014

Equals exp(arctanh(1/2)/2). - Amiram Eldar, Jul 10 2023

A011350 Decimal expansion of 6th root of 15.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

The 6th root r(6) of the expected value E(x^6) for a normal distribution with zero mean and standard deviation 1. See A289090 for more details. - Stanislav Sykora, Jul 26 2017

Ivan Panchenko, Table of n, a(n) for n = 1..1000

Cf. A011002, A076668, A289090, A289091.

RealDigits[Power[15, (6)^-1],10,120][[1]]  (* Harvey P. Dale, Apr 09 2011 *)

sqrtn(15, 6) \\ Michel Marcus, Jul 27 2017

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

Original entry on oeis.org

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

Stanislav Sykora, Jul 26 2017

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.

			1.44879190154930528525354659881281058821340103935196780729503058015...

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

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

// 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

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

a = (8*A076668)^(1/5).

cp's OEIS Frontend

A011002 Decimal expansion of 4th root of 3.

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A011350 Decimal expansion of 6th root of 15.

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

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula