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

1,2

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Amrik Singh Nimbran, Interesting infinite products of rational functions motivated by Euler, Math. Student, Vol. 85 (2016), pp. 117-133; ResearchGate link.

Index entries for algebraic numbers, degree 4.

Formula

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

From Amiram Eldar, Jun 28 2026: (Start)

Equals Product_{k>=1} (12*k-8)^2*(12*k-7)/((12*k-9)^2*(12*k-5)) (Nimbran, 2016, p. 130, eq. (50)).

Equals Product_{k>=1} (3*k-1)*(4*k-2)^2*(12*k-5)/((3*k-2)*(4*k-1)^2*(12*k-7)) (Nimbran, 2016, p. 130, eq. (51)). (End)

Example

1.3160740129524924608192189...

Mathematica

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

Prog

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

Crossrefs

Cf. A179615 (continued fraction).

Cf. A076668, A011350, A289090, A289091.

Sequence in context: A210621 A226771 A096614 * A298241 A113817 A197151

Adjacent sequences: A010999 A011000 A011001 * A011003 A011004 A011005

Keyword

nonn,cons,changed

Author

N. J. A. Sloane

Status

approved