cp's OEIS Frontend

A343054 Decimal expansion of the imaginary part of i^(1/12), or sin(Pi/24).

%I A343054 #32 Sep 05 2025 09:53:08
%S A343054 1,3,0,5,2,6,1,9,2,2,2,0,0,5,1,5,9,1,5,4,8,4,0,6,2,2,7,8,9,5,4,8,9,0,
%T A343054 1,0,1,9,3,7,4,0,7,0,4,8,1,1,7,3,2,2,5,1,8,9,0,6,1,6,9,4,8,3,3,5,1,3,
%U A343054 2,8,2,5,2,2,9,8,2,3,6,2,9,6,1,4,2,4,0,3,6,8,9,9,2,2,9,2,1,2,2,9,0,5,7,4,9,4,4,6,9,9,7,9,7,1,4,4
%N A343054 Decimal expansion of the imaginary part of i^(1/12), or sin(Pi/24).
%H A343054 Wikipedia, <a href="https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals">Trigonometric constants expressed in real radicals</a>
%H A343054 <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a>
%F A343054 Equals (1/2) * sqrt(2-sqrt(2+sqrt(3))).
%F A343054 This^2 + A144982^2 = 1. - _R. J. Mathar_, Aug 31 2025
%F A343054 Smallest positive root of 256*x^8-512*x^6+320*x^4-64*x^2+1=0. - _R. J. Mathar_, Aug 31 2025
%F A343054 Equals A019824/(2*A144982). - _R. J. Mathar_, Sep 05 2025
%e A343054 0.130526192220051591548...
%t A343054 RealDigits[Sin[Pi/24], 10, 100][[1]] (* _Amiram Eldar_, Apr 27 2021 *)
%o A343054 (PARI) imag(I^(1/12))
%o A343054 (PARI) sin(Pi/24)
%o A343054 (PARI) sqrt(2-sqrt(2+sqrt(3)))/2
%Y A343054 Cf. A144982 (cos(Pi/24)).
%K A343054 nonn,cons,easy,changed
%O A343054 0,2
%A A343054 _Seiichi Manyama_, Apr 04 2021