A182168 Decimal expansion of imaginary part of i^(1/4).

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

Offset

0,1

Comments

Also sin(Pi/8) or sine of 22.5 degrees.

The real part of i^(1/4) or cos(Pi/8) is A144981.

A quartic number of denominator 2 and minimal polynomial 8*x^4 - 8*x^2 + 1. - Charles R Greathouse IV, Jan 09 2022

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Michael Penn, The exact value of sin 5⅝°??, YouTube video, 2021.

Index entries for algebraic numbers, degree 4

Formula

Equals sqrt(2-sqrt(2)) / 2 = A101464/2. - Bernard Schott, Apr 12 2022

This^2 + A144981^2=1. - R. J. Mathar, Aug 31 2025

Smallest positive root of 8*x^4-8*x^2+1=0. - R. J. Mathar, Aug 31 2025

Example

0.382683432365089771728459984...

Maple

evalf(sin(Pi/8)) ; # R. J. Mathar, Jan 10 2013

Mathematica

RealDigits[Sqrt[2-Sqrt[2]]/2, 10, 120][[1]] (* G. C. Greubel, Sep 04 2022 *)

Prog

(PARI) sin(Pi/8) \\ Charles R Greathouse IV, Jan 09 2022
(SageMath) numerical_approx(sqrt(2-sqrt(2))/2, digits=120) # G. C. Greubel, Sep 04 2022

Crossrefs

Cf. A144981.

Sequence in context: A374971 A327951 A132019 * A086178 A388179 A016669

Adjacent sequences: A182165 A182166 A182167 * A182169 A182170 A182171

Keyword

nonn,cons

Author

Stanislav Sykora, May 16 2012

Status

approved