cp's OEIS Frontend

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

%I A182168 #39 Aug 31 2025 11:23:15
%S A182168 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,
%T A182168 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,
%U A182168 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
%N A182168 Decimal expansion of imaginary part of i^(1/4).
%C A182168 Also sin(Pi/8) or sine of 22.5 degrees.
%C A182168 The real part of i^(1/4) or cos(Pi/8) is A144981.
%C A182168 A quartic number of denominator 2 and minimal polynomial 8*x^4 - 8*x^2 + 1. - _Charles R Greathouse IV_, Jan 09 2022
%H A182168 G. C. Greubel, <a href="/A182168/b182168.txt">Table of n, a(n) for n = 0..10000</a>
%H A182168 Michael Penn, <a href="https://www.youtube.com/watch?v=y-8XbDLwzuo">The exact value of sin 5⅝°??</a>, YouTube video, 2021.
%H A182168 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F A182168 Equals sqrt(2-sqrt(2)) / 2 = A101464/2. - _Bernard Schott_, Apr 12 2022
%F A182168 This^2 + A144981^2=1. - _R. J. Mathar_, Aug 31 2025
%F A182168 Smallest positive root of 8*x^4-8*x^2+1=0. - _R. J. Mathar_, Aug 31 2025
%e A182168 0.382683432365089771728459984...
%p A182168 evalf(sin(Pi/8)) ; # _R. J. Mathar_, Jan 10 2013
%t A182168 RealDigits[Sqrt[2-Sqrt[2]]/2, 10, 120][[1]] (* _G. C. Greubel_, Sep 04 2022 *)
%o A182168 (PARI) sin(Pi/8) \\ _Charles R Greathouse IV_, Jan 09 2022
%o A182168 (SageMath) numerical_approx(sqrt(2-sqrt(2))/2, digits=120) # _G. C. Greubel_, Sep 04 2022
%Y A182168 Cf. A144981.
%K A182168 nonn,cons,changed
%O A182168 0,1
%A A182168 _Stanislav Sykora_, May 16 2012