A232738 Decimal expansion of the imaginary part of I^(1/8), or sin(Pi/16).

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

Offset

0,2

Comments

The corresponding real part is in A232737.

Links

Stanislav Sykora, Table of n, a(n) for n = 0..1000

Wikipedia, Trigonometric constants expressed in real radicals

Index entries for algebraic numbers, degree 8

Formula

Equals (1/2) * sqrt(2-sqrt(2+sqrt(2))). - Seiichi Manyama, Apr 04 2021

This^2 + A232737^2 = 1.

Smallest positive of the 8 real-valued roots of 128*x^8-256*x^6+160*x^4-32*x^2+1=0.

Equals A182168/(2*A232737). - R. J. Mathar, Sep 05 2025

Equals A272535/2. - R. J. Mathar, Jun 03 2026

Example

0.195090322016128267848284868477022240927691617751954807754502...

Mathematica

RealDigits[Sin[Pi/16], 10, 120][[1]] (* Harvey P. Dale, Sep 01 2018 *)

Prog

(PARI) imag(I^(1/8)) \\ Seiichi Manyama, Apr 04 2021
(PARI) sin(Pi/16) \\ Seiichi Manyama, Apr 04 2021
(PARI) sqrt(2-sqrt(2+sqrt(2)))/2 \\ Seiichi Manyama, Apr 04 2021
(Magma) R:= RealField(116); Sin(Pi(R)/16); // G. C. Greubel, Sep 20 2022
(SageMath) numerical_approx(sin(pi/16), digits=116) # G. C. Greubel, Sep 20 2022

Crossrefs

Cf. A232737 (real part), A010503 (imag(I^(1/2))), A182168 (imag(I^(1/4))), A019827 (imag(I^(1/5))), A019824 (imag(I^(1/6))), A232736 (imag(I^(1/7))), A019819 (imag(I^(1/9))), A019818 (imag(I^(1/10))).

Sequence in context: A199869 A378825 A197378 * A396976 A201395 A019881

Adjacent sequences: A232735 A232736 A232737 * A232739 A232740 A232741

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Nov 29 2013

Status

approved